MathDB
Very hard isogonality

Source: RMM Shortlist 2023 G3

February 29, 2024
Isogonal conjugategeometryRMM Shortlist

Problem Statement

A point PP is chosen inside a triangle ABCABC with circumcircle Ω\Omega. Let Γ\Gamma be the circle passing through the circumcenters of the triangles APBAPB, BPCBPC, and CPACPA. Let Ω\Omega and Γ\Gamma intersect at points XX and YY. Let QQ be the reflection of PP in the line XYXY . Prove that ∠BAP=∠CAQ\angle BAP = \angle CAQ.
Back to ProblemsView on AoPS