SOLUTION: how long is a chord that is 3 meters from the center of a circle with a radius of 5 meters?

Algebra ->  Circles -> SOLUTION: how long is a chord that is 3 meters from the center of a circle with a radius of 5 meters?       Log On


   

Question 878193: how long is a chord that is 3 meters from the center of a circle with a radius of 5 meters?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Imagine a circle, center at O, and the endpoints of the chord are on the circle at points A and B. A segment extends from point O and is perpendicular to the chord segment AB. Call this intersection point, which is also a perpendicular bisector, point P.

That description is of two right triangles sharing a side, OP. These values are known:
OP = 3;
OA = OB = 5.
You want to find values for AP or BP, and knowing just one of them, you know that AB=2AP=2BP.

Pythagorean Right Triangle Equation will let you solve for AP or BP.
3%5E2%2B%28AP%29%5E2=5%5E2
9%2BAP%5E2=25
AP%5E2=16
highlight%28AP=BP=4%29
The chord described, which is AB, is highlight%28AP%2BBP=4%2B4=8%29