MathDB
Interesting geo with tangents, external bisector and many equal segments

Source: Iberoamerican 2022, Day 2, P2

September 29, 2022
geometry

Problem Statement

Let ABCABC be an acute triangle with circumcircle Γ\Gamma. Let PP and QQ be points in the half plane defined by BCBC containing AA, such that BPBP and CQCQ are tangents to Γ\Gamma and PB=BC=CQPB = BC = CQ. Let KK and LL be points on the external bisector of the angle ∠CAB\angle CAB , such that BK=BA,CL=CABK = BA, CL = CA. Let MM be the intersection point of the lines PKPK and QLQL. Prove that MK=MLMK=ML.
Back to ProblemsView on AoPS