MathDB
China 2010 quiz3 problem 1

Source:

September 12, 2010
geometrysymmetrygeometric transformationangle bisector

Problem Statement

Let ABCDABCD be a convex quadrilateral with A,B,C,DA,B,C,D concyclic. Assume ∠ADC\angle ADC is acute and ABBC=DACD\frac{AB}{BC}=\frac{DA}{CD}. Let Γ\Gamma be a circle through AA and DD, tangent to ABAB, and let EE be a point on Γ\Gamma and inside ABCDABCD. Prove that AE⊥ECAE\perp EC if and only if AEAB−EDAD=1\frac{AE}{AB}-\frac{ED}{AD}=1.
Back to ProblemsView on AoPS