Let ABCDE be a convex pentagon such that the
triangles ABC, ACD, and ADE are similar.
The diagonals BD and CE intersect in point P.

Prove that the ray AP bisects side CD.

I have constructed a pentagon from 3 congruent isoceles triangles with equal angles of 75 degrees, with the long sides twice the length of the short one. Two are placed to form a parallelogram and the third forms a kite with the middle one, so that all angles are convex. To my dismay, it's pretty clear even by inspection that the ray does not bisect line CD.

I don't understand why such construction is not compliant with the problem. What am I missing?

Further assistance would be greatly welcomed.

Posted by broll on 2010-10-17 16:15:11