One interesting thing to notice is that the point C can be outside the segment AD, but then on the reversed direction " a^2=c^2+bd " what can be contemplated on the original theorem if we consider b or d to be negative.

This case is proven in the same way using the Pythagorean theorem or using the power of a point.

I bet you already knew that, but it would be a nice thing to say.

You lose. I did not.

> but it would be a nice thing to say.

Absolutely. Done that. Thank you.