Tutors Answer Your Questions about Circles (FREE)
Question 994568: a chord is 6 cm long. it is 15 cm from the centre of a circle. What is the radius of the circle.
Found 2 solutions by MathTherapy, josgarithmetic: Answer by MathTherapy(4047) (Show Source):
You can put this solution on YOUR website!
a chord is 6 cm long. it is 15 cm from the centre of a circle. What is the radius of the circle.
The perpendicular bisector is drawn from the circle's center to the chord, which it bisects
We now draw 2 radii to each endpoint of the chord
We now have an isosceles triangle which consists of 2 right triangles, with 2 radii as its hypotenuses.
To find the radius, we use the pythagorean theorem, and we get: . This results in a radius value of
Answer by josgarithmetic(13975) (Show Source):
You can put this solution on YOUR website! Imagine and draw a circle with center at the origin of cartesian system. yaxis makes a perpendicular bisector with a chord, and each part of the chord is 3 cm. in length. Two points on this circle are (3,15) and (3,15).
The question asks for the radius of the circle. How far is either of the specified (or found) points from the origina? That is the radius.
Use the Distance Formula.
Question 994217: A square has an area of 32cm2
What is the area of the largest circle that can fit in it ??
Answer by MathLover1(11324) (Show Source):
Question 989033: If y= mx + c is a tangents to the circle x^2 + y^2 =r^2,show that c = rsqrt(1 + m^2}}}. Hence, find the equations of the tangents to the circle x^2 + y^2 = 4 which pass through the points (0,+_6).
Answer by anand429(129) (Show Source):
You can put this solution on YOUR website! Centre of is (0,0) and radius r.
Since y=mx+c (or say mxy+c=0) is tangent to this circle, distance from centre(0,0) to this line is equal to radius
So,
=>
=> part (i)
Let y=mx+c be tangents to circle x^2 + y^2 = 4
Since, it passes through (0,6) and (0,6)
So,
6=0+c and 6 = 0+c
=> c=6 or 6
Now, using part(i) proof,
or
=> or (from both equationssame values of m)
So equation of tangents are
and and and
Since there are two external points, hence two tangents can be drawn from each point. So, we have got 4 equations of tangents.
Question 993955: the coordinates of a the center of a circle is (4,3).if the circle passes the origin what's the radius of the circle
Found 2 solutions by Alan3354, Boreal: Answer by Alan3354(47455) (Show Source):
You can put this solution on YOUR website! the coordinates of a the center of a circle is (4,3).if the circle passes the origin what's the radius of the circle

It's the distance from (0,0) to (4,3)
Answer by Boreal(1464) (Show Source):
You can put this solution on YOUR website! The center is at (4,3)
The radius can be determined by the fact that the point (0,0) is on the circle.
Distance formula or Pythagorean Theorem
sqrt (4^2+3^2)=sqrt (25)=5
radius is 5.
Question 993620: find the circumference of a circle with the diameter being 8
Answer by Cromlix(3061) (Show Source):
You can put this solution on YOUR website! Hi there,
Circumference of a circle = Pi x diameter
Circumference = Pi x 8
Circumference = 25.13 units (2 decimal places)
Hope this helps :)
Question 992576: A circle with center A and a radius of 5 is tangent to a larger circle with center B and a diameter three times that of the smaller circle. What is the distance from A to B?
Found 2 solutions by addingup, vleith: Answer by addingup(248) (Show Source):
You can put this solution on YOUR website! A has a radius of 5, and 5x2= a diameter of 10.
B has a diameter 3 times bigger, so 3x10= a diameter of 30 And 30/2= radius 15.
So, the distance of center A to center B, assuming that the circles are externally tangential, is 20. Look at the drawing I made you.
Answer by vleith(2950) (Show Source):
You can put this solution on YOUR website! circle A has a radius of 5 and a diameter of 10
Circle B has a diameter 3 times that of circle A. So B's diameter is 3*10 = 30.
That makes B's radius 30/2 = 15.
What is the length from B to A? 15 + 5 = 20
Question 992559: Please help me with this problem: Determine whether the equation x^2+y^24x+2y=9 represents a circle, a point, or no graph.
I know that if there's a graph it should represent a circle, but i'm having trouble factoring properly.
Thanks!
Answer by stanbon(69061) (Show Source):
You can put this solution on YOUR website! Determine whether the equation x^2+y^24x+2y=9 represents a circle, a point, or no graph.

Complete the square on the x and on the y terms::
x^24x+4 + y^2+2y+1) = 9+4+1

(x2)^2 + (y+1)^2 = 14

Circle with center at (2,1) and radius = sqrt(14)

Cheers,
Stan H.

Question 992303: QUESTION:In circle O, diameter AB is perpendicular to chord CD at E. If CD=20cm, BE=2cm and AE= 4x2, find the length of the diameter.
Using the intersecting chord theorem I know how to solve it, however neither values of CE or DE are given and you can't have two variables in an equation so I'm confused. By long shot i thought of using trigonometry but i don't think it's right. Thanks for the help in advance x
Answer by Theo(5548) (Show Source):
You can put this solution on YOUR website! the length of your diameter is 4x2 + 2 = 4x.
this means your radius is equal to 2x.
if CD is equal to 20, this means that CE and ED are both equal to 10 because a diameter cuts a chord perpendicular to it into 2 equal segments.
here's what you have:
AB = the diameter = 4x.
AO = a radius = 2x.
OB = a radius = 2x.
since EB is equal to 2, then OE must be equal to 2x2.
CE is equal to 10
ED is equal to 10
OC is equal to 2x because OC is a radius.
OD is equal to 2x because OD is a radius.
you have a right triangle formed that is OCE.
in that triangle:
OC is the hypotenuse which is equal to 2x.
OE is one leg which is equal to 2x2.
CE is the other leg which is equal to 10.
by pythagorus, OE^2 + CE^2 = OC^2 which becomes:
(2x2)^2 + 10^2 = (2x)^2
simplify this equation to get:
4x^2  8x + 4 + 100 = 4x^2
subtract 4x^2 from both sides of the equation to get:
8x + 4 + 100 = 0
add 8x to both sides of the equation to get:
4 + 100 = 8x
combine like terms to get:
104 = 8x
solve for x to get:
x = 13.
if x = 13, then:
OC = 2x = 26
OE = 2x2 = 24
CE = 10
by pythagorus, 10^2 + 24^2 = 26^2
this becomes:
100 + 576 = 676 which becomes:
676 = 676
this confirms the solution is correct.
you are asked to find the length of the diameter.
the length of the diameter is 4x which is equal to 4 * 13 which is equal to 52.
i believe that's your solution.
here's a picture to help you understand what i'm talking about.
the key to solving is to know the geometric relationship that a chord perpendicular to a diameter is cut in half.
you also needed to determine that the length of the diameters was 4x2 + 2 which made it equal to 4x.
you also needed to know that the triangle formed had a hypotenuse that was equal to the radius.
Question 992282: Complete the equation of the circle centered at (3 , 7 ) with radius 4.
Answer by macston(4006) (Show Source):
Question 991779: Given the circumference of a circle is 60 pi. Find the length of a 225 degree sector of this circle
Answer by Fombitz(25151) (Show Source):
Question 991385: Find the center and radius of the circle: x^2+y^24x+10y3=0
Found 4 solutions by Timnewman, ikleyn, josgarithmetic, Fombitz: Answer by Timnewman(249) (Show Source):
You can put this solution on YOUR website! Hi dear,
Comparing
x²+y²4x+10y3=0 with the general form of equation of a circle;x²+y²+2gx+2fy+c=0
From the above,
2g=4
g=2,
also,
2f=10
f=5
The centre of the
circle is (2,5).
Also,
r²=g²+f²c
r²=2²+5²(3)
r²=4+25+3
HOPE THIS HELPS?
Answer by ikleyn(988) (Show Source): Answer by josgarithmetic(13975) (Show Source): Answer by Fombitz(25151) (Show Source):
Question 990630: A circle is enclosed in a square. The diameter of the circle is 2x. The square has sides of length 3x. Find the area of the shaded region in terms of x. Keepy pi.
Thank you very much!
Answer by Timnewman(249) (Show Source):
Question 990600: The diameter of a circle has endpoints J(12,25) and K(10,13). Find the circumstance and area the circle. Use the pie key on your calculator and round to the nearest tenth.
Answer by Timnewman(249) (Show Source):
You can put this solution on YOUR website! Hi dear,
Use
Where y1=25,y2=13,x1=12,x2=10
put the above in the formula and get diameter of the circle to be 25.01
Now radius r=25.01/2
=12.51
circumference=2*pi*12.51
=78.61
area=pi*12.51²
=941.72
Question 990516: a circle has a center at (8,2). The point (3,7)is in the circle. What is the area of the circle to the nearest tenth of a square unit?
Answer by KMST(3791) (Show Source):
Question 990244: You have been asked to design a can shaped like a right circular cylinder with height h and radius r. Given that the can must hold exactly 170 cm^3, what values of h and r will minimise the total surface area (including the top and bottom faces)? Give your answers correct to 2 decimal places as a list [in brackets] of the form: [ h, r ]
for constants h (height), r (radius), in that order.
THANK YOU
Answer by josgarithmetic(13975) (Show Source):
Question 990255: A circle passes through the Point (8,7) and touches the yaxis at the Point (0,3). Find the equation of the circle. if the circle cuts the xaxis at D and E, find the equation of another circle which is DE as diameter.
Answer by josgarithmetic(13975) (Show Source):
You can put this solution on YOUR website! Unknown center of the first circle, (h,k).
Using Distance Formula
This circle touching, just touching, the yaxis at (0,3) means that the center is some point on the line y=3. This means, you can solve for h, because you know . This is based on knowing how the standard circle equation works.
Center of this first circle is therefore, (8,3). The point (0,3) on the circle may be the convenient point to again use the Distance Formula, to find the radius of this circle.
This first circle equation is then, .
I have not finished to do the final question, but maybe you can.
Question 990029: O is the center of the circle and m
Answer by Alan3354(47455) (Show Source):
Question 989575: what is the value of cot 0 and sec 15π/7?
Answer by Alan3354(47455) (Show Source):
You can put this solution on YOUR website! what is the value of cot 0
cot = 1/tan
tan(0) = 0
cot = 1/0 > infinity or undefined.
====================
and sec 15pi/7?
15pi/7 = 2pi  pi/7
sec(x) = sec(s) > sec(pi/7)
sec(pi/7) = 1/cos(pi/7)
I would use a calculator.
Question 987868: http://postimg.org/image/6omaybq21/
I tried approximating angle measures and ended up getting the right answer, J. However, I feel this is incorrect and would like to know a better way of solving it.
Answer by MathLover1(11324) (Show Source):
Question 987815: PLEASE HELP how do i start to solve this?
You upgraded the tires on your truck. The manufacturer tires are P245/70R16. You want upgraded to P285/75R16.
What is the diameter of the old tires?
What is the diameter of the new tires?
What is the circumference of the old tires?
What is the circumference of the new tires:
Answer by Alan3354(47455) (Show Source):
You can put this solution on YOUR website! You provide the specs of the tires.

The diameter of the old tires or the new tires is not a math problem.
Look it up somewhere and post it, or go away.
Question 987660: Hi again!!
A curve is traced by a point P(x,y) which moves such that its distance from the point A(1,1) is three times its distance from the point B(2,1). Determine the equation of the curve.
IF you can figure this out, congratulations. You can do college math and I can't. :) Due Tuesday.
Answer by josgarithmetic(13975) (Show Source):
You can put this solution on YOUR website! The Distance Formula is the key to starting this solution.
Distance PA is Distance PB*3
Simplify this equation and convert into any meaningful form through your arithmetic/algebra skills.
Question 987537: John wants to construct a fence around his farm.
The farm is circular in shape with a radius of 1 ft.
What is the length of fencing material he will need to fence one complete circle around his farm?
Answer by josgarithmetic(13975) (Show Source):
Question 987278: PLEASE HELP ME
You upgraded the tires on your truck. The manufacturer tires are P245/70R16. You want upgraded to P285/75R16.
What is the diameter of the old tires?
What is the diameter of the new tires?
What is the circumference of the old tires?
What is the circumference of the new tires:
If your odometer says you have traveled 15,000 miles, how far have you actually traveled with the new tires?
If your speedometer reads 70mph, can you get a ticket for going 5mph or more over the speed limit?
Answer by Alan3354(47455) (Show Source):
Question 986902: Please help me solve this.The outside of a cylindrical structure at a factory must be painted.it radius is 3,5 m and its height is 8 m.How many litres of paint must be bought if 1 litre covers 10 m(2)?(the bottom of the structure will not be painted.)
Answer by Cromlix(3061) (Show Source):
You can put this solution on YOUR website! Hi there,
I assume the top of the cylinder will be painted
but, not the bottom.
Surface area of a cylinder
= pi* r^2 + 2* pi *r *h
= pi* 3.5^2 + 2 *pi *3.5* 8 (* times)
= 38.49 + 175.93
 214.42 m^2
No. of litres required:
= 214.42/10
= 21.4 litres.
Hope this helps :)
Question 986754: I really need help with this, would appreciate any help.
Show that the point E(1 , 2) lies on the circumference of the circle with equation
x2 + y2 – 2x – 3y – 1 = 0 and find the coordinates of the point F,
given that EF is a diameter.
Answer by Fombitz(25151) (Show Source):
Question 986443: Points O(0,0) and B(0,3) below lie in the standard (x,y) coordinate plane. The collection of all points such that each is twice as far from B as from O forms a circle. The point (sqrt 3, 0) is 1 point on the circle. What are the coordinates of the center of the circle?
F. (sqrt 3/2, 3/2)
G. (0,3/2)
H. (0, 1)
J. (0,1)
K. (0,3)
Answer by josgarithmetic(13975) (Show Source):
You can put this solution on YOUR website! You are saying Distance between (x,y) and B(0,3) is 2 times distance between (x,y) and O(0,0). You are expecting, according to description, the points (x,y) are a circle.
Want standard form, requiring Completing the Square
Circle, centered at (0,1), and radius is .
Question 986087: An arc of a circle of radius 7cm is 14cm long.what does d arc subtend at d centre of d circle
Found 2 solutions by Alan3354, josgarithmetic: Answer by Alan3354(47455) (Show Source):
You can put this solution on YOUR website! An arc of a circle of radius 7cm is 14cm long.what does d arc subtend at d centre of d circle

Angle = Arc/r = 14/7 = 2 radians
Answer by josgarithmetic(13975) (Show Source):
Question 985805: The angle subtended by a chord at the centre of a circle is
Answer by ikleyn(988) (Show Source):
Question 985461: The points X(3,4) and Y(9,1) lie on the circumference of a circle. There is exactly 60 degree of arc between X and Y. Find the radius of the circle.
Found 2 solutions by MathTherapy, josgarithmetic: Answer by MathTherapy(4047) (Show Source): Answer by josgarithmetic(13975) (Show Source):
Question 985460: Points A, B, and C lie on the circumference of a circle. AB is twice the radius of the circle. Find m(angle)ACB.
Answer by ikleyn(988) (Show Source):
You can put this solution on YOUR website!
Answer. 90°.
Solution
Since AB is twice the radius of the circle, AB is the diameter of the circle.
The angle LACB is 90°, because it leans on the diameter.
Question 985245: The formula for the circumference of the basketball is c=2pi(r). If the circumference of a basketball is 29inches is it a regulation size basketball?
The Radius is 4.78
Answer by ikleyn(988) (Show Source):
You can put this solution on YOUR website!
BASKETBALL SIZES
SIZE BEST FOR CIRCUMFERENCE
7 Men's Official Men, boys 12 and older 29 1/2  30 in 75  76 cm
6 Women's Official Women, girls 7 and older, boys ages 712 28 1/2  29 in 72  74 cm
5 Youth Kids under 7 27  28 in 69  71 cm
3 Mini Miniature basketball best for small kids 22  22.5 in 56  57 cm
From GOOGLE.
Key words "regular size basketball".
It is much easier to find it in GOOGLE than to print and to submit the huge text to this site. Isn't?
Question 985135: 16. The circumference of the circular pool is 31.4m. The path around it is 1m wide. Find the circumference of the outer boundary of the path.
Answer by macston(4006) (Show Source):
Question 985081: a circle has a center (8,2). the point (3,7) is on the circle. What is the area of the circle to the nearest tenth of a square unit?
Answer by Alan3354(47455) (Show Source):
You can put this solution on YOUR website! a circle has a center (8,2). the point (3,7) is on the circle. What is the area of the circle to the nearest tenth of a square unit?

Find the distance between the points. That's the radius r.
Question 985080: a circle has a center (3,5). the point (3,8) is on the circle. What is the circumference of the circle to the nearest unit?
Answer by macston(4006) (Show Source):
Question 985052: Give the equation of the circle tangent to both axes, of radius 5 and in the 1st quadrant. In the 2nd Quadrant.In the 3rd quadrant. In the 4th quadrant.
Answer by macston(4006) (Show Source):
You can put this solution on YOUR website! .
The distance from each axis to center of circle must equal radius for the circle to be tangent to both axes.
.
In the first quadrant, center of circle is +5 from each axis, center at (5,5)
.
In second quadrant, center of circle is +5 from y axis (x=5) and 5 below x axis (y=5), center at (5,5)
.
In third quadrant, center of circle is 5 left of y axis (x=5) and 5 below x axis (y=5), center at (5,5)
.
In fourth quadrant, center of circle is 5 left of y axis (x=5), 5 above x axis (y=5), center at (5,5)
.
Standard form of circle:
where (h,k) is the center and r is the radius
.
First quadrant: h=5; k=5; r=5
.
Second quadrant: h=5; k=5; r=5
.
Third quadrant: h=5; k=5; r=5
.
Fourth quadrant: h=5; k=5; r=5
Question 985050: Find the equation of circle having (10,2) and (6,4) as ends of diameter.
Answer by Cromlix(3061) (Show Source):
You can put this solution on YOUR website! Hi there
First find the mid point of the
diameter. This will give you the
centre of the circle.
Mid point = x1 + x2/2, y1 + y2/2
Mid point = 10 + 6/2 , 2 + (4)/2
Mid point = 16/2 , 2/2
Mid point = 8 , 1
Distance from (8,1) to (10,2)
will give the radius
Distance formula = √(x2  x1)^2 + (y2  y1)^2
Distance formuls = √(10  8)^2 + (2(1))^2
Distance formula = √(2)^2 + (3)^2
Distance formula = √ 4 + 9
Distance formula = √ 13
Radius = √13
Circle formula:
(x  a)^2 + (y  b)^2 = r^2
Using Midpt (8, 1) and radius = √13
(x  8)^2 + (y + 1)^2 = 13
Hope this helps :)
Question 984845: A circle has a center (3,6) and radius 8. Find all values of y such that (2, y) is a point on the circle.
may be more than one answer list smaller then larger
Provide exact expressions, not decimal approximations.
Answer by Alan3354(47455) (Show Source):
You can put this solution on YOUR website! A circle has a center (3,6) and radius 8. Find all values of y such that (2,y) is a point on the circle.

The circle is
Sub 2 for x and find y (2 values).

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