MathDB
Isosceles trapezoid geo asking to prove concurrency

Source: St Petersburg 2021 11.6

December 23, 2021
geometrytrapezoidcircumcircleangle bisector

Problem Statement

Point MM is the midpoint of base ADAD of an isosceles trapezoid ABCDABCD with circumcircle ω\omega. The angle bisector of ABDABD intersects ω\omega at KK. Line CMCM meets ω\omega again at NN. From point BB, tangents BP,BQBP, BQ are drawn to (KMN)(KMN). Prove that BK,MN,PQBK, MN, PQ are concurrent.
A. Kuznetsov
Back to ProblemsView on AoPS