MathDB
Concyclic points

Source: All russian olympiad 2016,Day1,grade 9,P2

May 1, 2016
geometryConcyclicgeometry proposed

Problem Statement

ω\omega is a circle inside angle ∡BAC\measuredangle BAC and it is tangent to sides of this angle at B,CB,C.An arbitrary line ℓ \ell intersects with AB,ACAB,AC at K,LK,L,respectively and intersect with ω\omega at P,QP,Q.Points S,TS,T are on BCBC such that KS∥ACKS \parallel AC and TL∥ABTL \parallel AB.Prove that P,Q,S,TP,Q,S,T are concyclic.(I.Bogdanov,P.Kozhevnikov)
Back to ProblemsView on AoPS