I’m going to be doing a geometry review with my younger son this year. He’s studied a bit of geometry before so we’ll probably just be bouncing around with various different topics. Today I thought introducing the power of a point would be a fun way to get going with this project.

Before starting the project today we looked at the definition on Wikipedia. Then we started chatting.

The first thing I asked him to prove was that the power of a point was equal to the square of the length of the tangent drawn from the point to the circle. He did a really nice job with this proof:

Next up was a slightly more complicated formula – the power of a point is also equal to the product of two distances – the distance from the point to the closest part of the circle multiplied by the distance from the point to the point on the circle that is the farthest away. This proof gave him a lot more trouble, but I think it is really interesting to see what it looks like when a kid is struggling through a proof.

He hadn’t quite made it through the proof in the last section by 8 min so I just started a new video. He he finished up and we talk about some of the interesting ideas we’ll encounter while we study more about the power of a point: