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| Math Central | Quandaries & Queries |
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Subject: finding a radius I have the length of the cord and the distance from the cord to the arc, is it possible to find the radius with just these parameters? |
Kevin,
I let c be the length of the cord, h be the height of the arc above the centre of the cord and r be the radius of the circle.
In the diagram the triangle PQR is a right triangle and hence by Pythagoras' Theorem
(c/2)2 + (r - h)2 = r2
Simplifying this becomes
c2/4 + r2 - 2hr + h2 = r2 or
r = (4h2 + c2)/(8h)
Penny
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