MathDB
Conditional geometry with a right angle

Source: BMO SL 2023 G6

May 3, 2024
geometryAZE BMO TSTTSTBMO Shortlist

Problem Statement

Let ABCABC be an acute triangle (AB<BC<ACAB < BC < AC) with circumcircle Γ\Gamma. Assume there exists X∈ACX \in AC satisfying AB=BXAB=BX and AX=BCAX=BC. Points D,E∈ΓD, E \in \Gamma are taken such that ∠ADB<90∘\angle ADB<90^{\circ}, DA=DBDA=DB and BC=CEBC=CE. Let PP be the intersection point of AEAE with the tangent line to Γ\Gamma at BB, and let QQ be the intersection point of ABAB with tangent line to Γ\Gamma at CC. Show that the projection of DD onto PQPQ lies on the circumcircle of △PAB\triangle PAB.
Back to ProblemsView on AoPS