MathDB
AL + JB = LJ wanted, cyclic ABCD, angle bisectors

Source: OLCOMA Costa Rica National Olympiad, Final Round, 2016 Shortlist G2 day2

September 25, 2021
geometrycyclic quadrilateral

Problem Statement

Let ABCDABCD be a convex quadrilateral, such that A A, B B, CC, and DD lie on a circle, with ∠DAB<∠ABC\angle DAB < \angle ABC. Let II be the intersection of the bisector of ∠ABC\angle ABC with the bisector of ∠BAD\angle BAD. Let ℓ\ell be the parallel line to CDCD passing through point II. Suppose ℓ\ell cuts segments DADA and BCBC at L L and JJ, respectively. Prove that AL+JB=LJAL + JB = LJ.
Back to ProblemsView on AoPS