Thread: geometry question

Given unit circle P. Points A and B are on the circle (r=1), forming an acute angle APB (theta). What line segment is equal to the tangent theta if line segment DC is tanget to circle at point b.

Hello, Pat722!

The directions are somewhat fuzzy.
I may have misinterpreted them.

I believe the diagram looks like this:

Code:

                          E
                          o
                         .:
                        . :
                       .  :
              * * *  A.   :
          *          o    o D
        *           /   * |
       *         1 /     *|
                  /       |
      *          / @      *
      *         o - - - - o B
      *       P      1    *
                          |
       *                 *|
        *               * |
          *           *   o
              * * *       C

We have the unit circle with center and radii

is tangent to the circle at
Extend to meet extended at

Then: .

Therefore: .