MathNet 2010 — Part 04 Question 89

In an isosceles triangle $ABC$ with $AC=BC$, the incircle touches $BC,CA,AB$ at $A',B',C'$, respectively. Segment $AA_1$ meets the incircle at $D$, and line $B'D$ meets side $AB$ at $E$. Prove that $AE=EC'$.