Proving two circles are orthogonal

[jdinatale]

Homework Statement

Homework Equations

The Attempt at a Solution

Here's an image of what I need to show.

I know I need to show that the segment from the center of the smaller circle to F forms a right angle with line segment CF. Alternatively I could show that line segment CH forms a right angle with the line segment from the center of the smaller circle to H. Both of those methods seem unlikely, since the center of the smaller circle isn't even included in the original image in my textbook.

I noticed the the Power of point E is EF*EA which equals EH*EB. I also noticed that $\angle AFB = \angle AHB = 90^\circ$

I also have the secant-secant angle theorem, but that doesn't seem to help, because we don't know the measure of the intercepted arcs, plus that doesn't seem really useful anyways.

I also don't have access to inverses, so I can't use those.

 

[susskind_leon]

Can you use Pythagoras' theorem?