Problem 8

Given: Circle and circle are tangent at D. The length of the radius of

circle is r. .

Prove: .

[Problem submitted by Steve Lee, LACC Professor of Mathematics.]

Solution:

Draw line segments and . Since , and are on a circle.

Therefore, . Also, because they face the same arc, .

Therefore, (1).

Since , .

Therefore, .

So, (2).

By (1) and (2) .