MathDB

2

Part of 2013 ITAMO

Problems(1)

M is the midpoint of AB, incircles of ACM, BCM

Source: Itamo 2013, problem 2

5/17/2013
In triangle ABCABC, suppose we have a>ba> b, where a=BCa=BC and b=ACb=AC. Let MM be the midpoint of ABAB, and α,β\alpha, \beta are inscircles of the triangles ACMACM and BCMBCM respectively. Let then A′A' and B′B' be the points of tangency of α\alpha and β\beta on CMCM. Prove that A′B′=a−b2A'B'=\frac{a - b}{2}.
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