Problem

Source: India TST 2023 Day 4 P1

Tags: geometry, TST



Suppose an acute scalene triangle ABC has incentre I and incircle touching BC at D. Let Z be the antipode of A in the circumcircle of ABC. Point L is chosen on the internal angle bisector of BZC such that AL=LI. Let M be the midpoint of arc BZC, and let V be the midpoint of ID. Prove that IML=DVM