Geometry Refresher

Brilliant Geometry Puzzle
Andy Math

I am a sucker for math problems. I like the ones that are easy for me to solve, I don't much care for the really esoteric stuff, i.e. problems I can't easily solve. I started watching this video and I'm thinking I should be able to solve this. I attack with the Pythagorean Formula (which is basically the only tool in my geometry toolbox) but I get nowhere. So I resume watching to see how he is going to solve it and he immediately brings up the Intersecting Chords Theorem. The what? Never heard of it. What the heck is this thing? So, more YouTube:

Intersecting Chords Theorem! (explanation and examples)
You Can Learn Math with Alyssa

I like Alyssa, she moves a little too slowly for my taste, but she is crystal clear and she has a pleasant voice. But then she comes to Central Angles and Inscribed Angles and my brain objects, so more YouTube:

Central Angles and Inscribed Angles! (theorems AND examples)
You Can Learn Math with Alyssa

Alyssa explains what the theorem is and shows how to apply it, but she doesn't explain how the theorem is derived, what some people call 'a proof', so now we need another explanation.

Inscribed angle theorem proof | High School Geometry | High School Math | Khan Academy
Khan Academy

Now that I think about it, I probably learned about all this back in high school, but I think that was it for geometry. After that is was calculus, trig and matrices, and geometry kind of got left in the dust.