Question

The picture below shows part of a circle:

What is the radius of the circle?

Answer 1

First, complete the circle. Draw BD and join one of its end D to C. ∠BAC + ∠BDC= 180° ∠D = 40°, ∠BCD (angle on semicircle). 

So ABCD is right-angled.

sin 40 = \(\frac{8}{BD}\)

BD = \(\frac{8}{sin\,40}\) = \(\frac{8}{0.6428}=12.44\)

Radius = \(\frac{12.4}{2}\) = 6.2 cm