Math Help - Geometry proof help please?

Imageshack - circlesg.jpg

There are two circles touching at C. The larger has midpoint B, the smaller goes through B. Prove that any chord [AB] of the circle is bisected by the smaller circle.

I can prove that angle AEC and angle BDC are 90 degrees, and that AB:BC = 1:1

How do I prove the rest?

-DLA

2. Originally Posted by DarkLightA
Imageshack - circlesg.jpg

There are two circles touching at C. The larger has midpoint B, the smaller goes through B. Prove that any chord [AB] of the circle is bisected by the smaller circle.

I can prove that angle AEC and angle BDC are 90 degrees, and that AB:BC = 1:1

How do I prove the rest?

-DLA
Triangle AEC and BDC are right angled triangles, and AE is parallel to BD. Since AB = BC, ED = DC. It is true for any chord.