SOLUTION: the center of a circle is at (-3,2) and its radius is 7. Find the length of the chord, which is bisected at (3, 1).

Algebra ->  Length-and-distance -> SOLUTION: the center of a circle is at (-3,2) and its radius is 7. Find the length of the chord, which is bisected at (3, 1).       Log On


   

Question 1184227: the center of a circle is at (-3,2) and its radius is 7. Find the length of the chord, which is bisected at (3, 1).
Found 2 solutions by ikleyn, MathLover1:
Answer by ikleyn(52787) About Me  (Show Source):
You can put this solution on YOUR website!
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the center of a circle is at (-3,2) and its radius is 7. Find the length of the chord, which is bisected at (3, 1).
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The distance between the given points is  sqrt%286%5E2%2B1%5E2%29 = sqrt%2837%29.


It is the length of the leg of the right angled triangle, whose hypotenuse is 7.


THEREFORE, half of the chord's length is  sqrt%287%5E2-37%29 = sqrt%2849-37%29 = sqrt%2812%29 = 2%2Asqrt%283%29.


The entire chord is twice this length, or  4%2Asqrt%283%29.    ANSWER

Solved.



Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

the center of a circle is at (-3,2) =>h=-3 and k=2
and its radius is r=7
equation is:
%28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2
%28x-%28-3%29%29%5E2%2B%28y-2%29%5E2=7%5E2
%28x%2B3%29%5E2%2B%28y-2%29%5E2=49

Find the length of the chord, which is bisected at (3,+1)


if the chord is bisected at (3,+1), find solutions for intersection of the circle with vertical line x=3
circle

A is the midpoint+of the chord so angle CAB is a right angle.
Use coordinates (-3,2) and (3,1) to find the length of the line segment CA.
Now you can use Pythagoras theorem to find the length of the line segment AB, which is half the length of the chord.
CA=distance between points (-3,2) and (3,1)
CA=sqrt%28%283-%28-3%29%29%5E2%2B%281-2%29%5E2%29
CA=sqrt%286%5E2%2B1%5E2%29
CA=sqrt%2837%29+
CB=7
%28AB%29%5E2=7%5E2-%28sqrt%2837%29+%29%5E2
%28AB%29%5E2=49-37
%28AB%29%5E2=12
AB+=sqrt%2812%29
AB+=2sqrt%283%29 -> half the length of the chord
the length of the chord will be 4sqrt%283%29+=>answer