MathDB
PQ tangent to circumcircle of ABC

Source: Mediterranean Mathematical Olympiad 2022 P4 MMC

September 21, 2022
geometrytangent

Problem Statement

The triangle ABCABC is inscribed in a circle γ\gamma of center OO, with AB<ACAB < AC . A point DD on the angle bisector of ∠BAC\angle BAC and a point EE on segment BCBC satisfy OEOE is parallel to ADAD and DE⊥BCDE \perp BC. Point KK lies on the extension line of EBEB such that EA=EKEA = EK. A circle pass through points A,K,DA,K,D meets the extension line of BCBC at point PP, and meets the circle of center OO at point Q≠AQ\ne A. Prove that the line PQPQ is tangent to the circle γ\gamma.
Back to ProblemsView on AoPS