SOLUTION: express the length l of a chord of a circle of radius 5 as a function of its distance x from the centre of the circle, and determine the domain of the function
Algebra.Com
Question 988668: express the length l of a chord of a circle of radius 5 as a function of its distance x from the centre of the circle, and determine the domain of the function
Found 2 solutions by Boreal, solver91311:
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
It helps to draw this.
The chord's length is twice the sqrt (25-x^2). The radius is the hypotenuse, the distance from the center and half the chord's length are the two legs.
y=2*sqrt(25-x^2)
domain of x is ([0,5].
At 0, we have the diameter, or 10.
At 5, we have a tangent to the circle and length 0.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Construct a radius to one endpoint of the chord. Construct another radius that intersects the chord at its midpoint. You should now have a right triangle, hypotenuse that measures 
(the radius of the circle), one leg that measures 
(the distance from the center of the circle to the chord), and the other leg that measures one-half of the measure of the chord length.
Use the Pythagorean Theorem to derive your function. The domain of the function will be \right)\ =\ \left\{x\ \in\ \mathbb{R}\ :\ 0\ \leq\ x\ <\ r\right\})
It is ok for to equal zero because the diameter of a circle is just a special case of a chord. However, cannot be equal to the radius of the circle because your can't have a chord of zero length.
John
My calculator said it, I believe it, that settles it
RELATED QUESTIONS
SOLUTION: express the length l of a chord of a circle of radius 8 in. as a function of... (answered by ikleyn)
The distance of a chord of a circle of radius 5 centimetre from the centre of the circle... (answered by ikleyn)
Express the length L of a chord of a circle with radius 10cm as a function of the... (answered by Edwin McCravy)
A circle has radius 5 and centre (2, 4). The point (3,2) is the midpoint of a chord of... (answered by MathLover1,MathTherapy)
the distance of a chord of a circle of a radius 5cm from the centre of the circle is 4 cm (answered by Boreal)
In a circle of radius 13 cm the length of its chord is 10 cm. Find the perpendicular... (answered by josgarithmetic)
a chord is drawn away from the centre of a circle of radius 5cm.calculate the length of... (answered by Theo,greenestamps)
a chord 8cm from centre of circle of a radius 11cm find the length of the chord (answered by ikleyn)
In a circle of radius5cm,a chord measuring 8cmhas been drawn,find its distance from the... (answered by hokies)