MathDB
(AC=BC, P,Q in AB): <PCQ \le <ACB /2 => PQ\le AB/2

Source: Tuymaada Junior 2001 p6

April 30, 2019
geometrygeometric inequalityisoscelesIsosceles Triangle

Problem Statement

On the side ABAB of an isosceles triangle ABAB (AC=BCAC=BC) lie points PP and QQ such that ∠PCQ≤12∠ACB\angle PCQ \le \frac{1}{2} \angle ACB. Prove that PQ≤12ABPQ \le \frac{1}{2} AB.
Back to ProblemsView on AoPS