MathDB
Center on BC

Source: Kazakhstan National Olympiad 2024 (9 grade), P5

March 21, 2024
geometry

Problem Statement

In triangle ABCABC (AB≠ACAB\ne AC), where all angles are greater than 45∘45^\circ, the altitude ADAD is drawn. Let ω1\omega_1 and ω2\omega_2 be-- circles with diameters ACAC and ABAB, respectively. The angle bisector of ∠ADB\angle ADB secondarily intersects ω1\omega_1 at point PP, and the angle bisector of ∠ADC\angle ADC secondarily intersects ω2\omega_2 at point QQ. The line APAP intersects ω2\omega_2 at the point RR. Prove that the circumcenter of triangle PQRPQR lies on line BCBC.
Back to ProblemsView on AoPS