Quandaries and Queries
  

 

I am a software developer and I having a problem that I need some assistance with.

If given the length of a chord (121”) and the distance from the midpoint of the arc to the midpoint of a chord (12”), how would I find the length of the radius?

Thanks,
Stace
 

 

Hi Stace,

I want to solve this problem in general, that is for a chord of length c and an arc that is h units in height at the midpoint of the chord. In the diagram below r is the radius of the circle, B is the midpoint of the chord and C is the centre of the circle and hence triangle ABC is a right triangle.

Thus by Pythagoras Theorem

(r - h)2 + ( c/2 )2 = r2

Thus

r2 - 2rh + h2 + ( c/2 )2 = r2

so

In your situation with c = 121 inches and h = 12 inches

Penny