@The-Rogue-Blade This is a good question! If we take the Power of a Point Theorem literally, then the segments that we are multiplying together should live up to the name "Power of a Point"; they should all emanate from the same point.

M2W2D8-y-part-2-power-of-point-why-not-ae-times-af-equals-bc-squared.png

In the above illustration, the correct answer is shown:

$$CF \times CE = (BC)^2$$

Now consider $$\overline{AE}$$ and $$\overline{AF};$$ these segments emanate from point $$A,$$ but the segment $$\overline{BC}$$ emanates from a $$\textcolor{red}{\text{different}}$$ point, $$C.$$ We have not one point, but $$2$$ points.

M2W2D8-y-part-2-power-of-point-why-not-ae-times-af-equals-bc-squared2.png

Unfortunately, it's not called "Power of Two Points," so

$$AE \times AF \neq (BC)^2$$

🙂