MathDB
China Mathematical Olympiad 2020 Q2

Source: China Mathematical Olympiad 2020 Q2

November 26, 2019
geometry

Problem Statement

In triangle ABCABC, AB>AC.AB>AC. The bisector of ∠BAC\angle BAC meets BCBC at D.D. PP is on line DA,DA, such that AA lies between PP and DD. PQPQ is tangent to ⊙(ABD)\odot(ABD) at Q.Q. PRPR is tangent to ⊙(ACD)\odot(ACD) at R.R. CQCQ meets BRBR at K.K. The line parallel to BCBC and passing through KK meets QD,AD,RDQD,AD,RD at E,L,F,E,L,F, respectively. Prove that EL=KF.EL=KF.
Back to ProblemsView on AoPS