MathDB
Angle Equality

Source: Turkey TST 2014 Day 3 Problem 7

March 12, 2014
trigonometrygeometry proposedgeometry

Problem Statement

Let PP be a point inside the acute triangle ABCABC with m(PAC^)=m(PCB^)m(\widehat{PAC})=m(\widehat{PCB}). DD is the midpoint of the segment PCPC. APAP and BCBC intersect at EE, and BPBP and DEDE intersect at QQ. Prove that sin⁡BCQ^=sin⁡BAP^\sin\widehat{BCQ}=\sin\widehat{BAP}.
Back to ProblemsView on AoPS