MathDB
Yet another incenter problem

Source: India IMOTC 2024 Day 3 Problem 1

May 31, 2024
geometryincenter

Problem Statement

Let ABCABC be an acute-angled triangle with AB<ACAB<AC, incentre II, and let MM be the midpoint of major arc BACBAC. Suppose the perpendicular line from AA to segment BCBC meets lines BIBI, CICI, and MIMI at points PP, QQ, and KK respectively. Prove that the A−A-median line in △AIK\triangle AIK passes through the circumcentre of △PIQ\triangle PIQ.
Proposed by Pranjal Srivastava and Rohan Goyal
Back to ProblemsView on AoPS