Power Of A Point

Hint for #6

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

Two More Theorems

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