SOLUTION: A chord 16cm long is perpendicular to the radius of a circle. The distance of the intersection of the chord and the radius to the outer end of the radius is 2cm. What is the radius

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Question 621624: A chord 16cm long is perpendicular to the radius of a circle. The distance of the intersection of the chord and the radius to the outer end of the radius is 2cm. What is the radius of the circle?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A chord 16cm long is perpendicular to the radius of a circle.
The distance of the intersection of the chord and the radius to the outer end of the radius is 2cm.
What is the radius
:
Draw this out
let x = the distance from center to the intersection of the radius thru the chord
then the radius: r = x+2
:
The radius is equal the hypotenuse of a right triangle with legs of 8 and x
r =sqrt%288%5E2%2Bx%5E2%29
We also know that r = x+2, therefore
x + 2 = sqrt%2864+%2B+x%5E2%29
Square both sides
(x+2)^2 = 64 + x^2
FOIL (x+2)(x+2)
x^2 + 4x + 4 = 64 + x^2
subtract x^2 from both sides
4x + 4 = 64
4x = 64 - 4
4x = 60
x = 60/4
x = 15
therefore
r = 15 + 2 = 17 cm is the radius