I have the following problem: Two circles (middle points $A,C$) have two intersections: $E,F$. Now we draw a common tangent on the circles and we'll get $G,H$. Let $I:=GH \cap EF$. Now I have to proof $GI=IH$.
I made this drawing:
and I tried to find some common angles or sides to use congruences, but I wasn't able to find some, because I have differnt circles with different radius'.
Perhaps someone can give me a hint how to move on? Thanks in advance.