MathDB
Variable line touches a fixed circle

Source: VII Caucasus Mathematical Olympiad

March 13, 2022
geometry

Problem Statement

Point PP is chosen on the leg CBCB of right triangle ABCABC (∠ACB=90∘\angle ACB = 90^\circ). The line APAP intersects the circumcircle of ABCABC at point QQ. Let LL be the midpoint of PBPB. Prove that QLQL is tangent to a fixed circle independent of the choice of point PP.
Back to ProblemsView on AoPS