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Slightly weird points which are not so weird

Source: India TST 2023 Day 4 P1

July 9, 2023
geometryTST

Problem Statement

Suppose an acute scalene triangle ABCABC has incentre II and incircle touching BCBC at DD. Let ZZ be the antipode of AA in the circumcircle of ABCABC. Point LL is chosen on the internal angle bisector of ∠BZC\angle BZC such that AL=LIAL = LI. Let MM be the midpoint of arc BZCBZC, and let VV be the midpoint of IDID. Prove that ∠IML=∠DVM\angle IML = \angle DVM
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