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Angles in a isosceles trapezoid

Source: 2015 Korean Mathematical Olympiad P6

November 1, 2015
geometrytrapezoidcircumcircle

Problem Statement

An isosceles trapezoid ABCDABCD, inscribed in ω\omega, satisfies AB=CD,AD<BC,AD<CDAB=CD, AD<BC, AD<CD. A circle with center DD and passing AA hits BD,CD,ωBD, CD, \omega at E,F,P(≠A)E, F, P(\not= A), respectively. Let AP∩EF=QAP \cap EF = Q, and ω\omega meet CQCQ and the circumcircle of △BEQ\triangle BEQ at R(≠C),S(≠B)R(\not= C), S(\not= B), respectively. Prove that ∠BER=∠FSC\angle BER= \angle FSC.
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