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Prove CD^2=BDxCE

Source: China Second Round 2015 (B) Q2

May 5, 2016
geometryincenter

Problem Statement

In isoceles △ABC\triangle ABC, AB=ACAB=AC, II is its incenter, DD is a point inside △ABC\triangle ABC such that I,B,C,DI,B,C,D are concyclic. The line through CC parallel to BDBD meets ADAD at EE. Prove that CD2=BD⋅CECD^2=BD\cdot CE.
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