MathDB
Length of segments

Source: 2022 IZHO P4, https://izho.kz/contest/problems/

February 18, 2022
geometryincenter

Problem Statement

In triangle ABCABC, a point MM is the midpoint of ABAB, and a point II is the incentre. Point A1A_1 is the reflection of AA in BIBI, and B1B_1 is the reflection of BB in AIAI. Let NN be the midpoint of A1B1A_1B_1. Prove that IN>IMIN > IM.
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