When I prove the relationship I find between (AP)(BP) and (CP)(DP), I like to draw segments AC and BD.[br][br]I also use the Inscribed Angle Theorem.

In the next figure, the brown triangle has side lengths a, b, c.[br][br]1. First, explain why the lengths written for the green, purple, and orange segments are correct.[br][br]2. In the initial configuration, PB=c+a. (Why?)[br][br]3. How long are segments PA, PC, and PD?[br][br]4. What does the Power of a Point Theorem say about a, b, c, and [math]\theta[/math]?[br][br]5. Click "Right it up!" and answer the same question (although [math]\theta[/math] drops out of the equation).[br][br]