I need help with a geometry proof.

Question

Given: segment AC is congruent to segment to segment EC and segment AE is perpendicular to segment FG.

Prove: Circle A is congruent to circle E

 

  

Answer 1

So segment AE joins the centers of the circles.

C is the midpoint of AE as given and A,B,C,D,E are

on segment AE (obviously) with B and D are the

tangent points of the circles.

 

Since FG is perpendicular to AE through C, there are

2 right triangles formed: ACF and ECF.

 

These right triangles are congruent by LL, as CF is congruent to itself

by reflexive property

 

Then AF and EF are congruent, CPCTC

which are the radii of the circle.

 

Since the radii are the same, the circles are congruent.