MathDB

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

Source: Itamo 2013, problem 2

May 17, 2013

geometrygeometry proposed

Problem Statement

In triangle

ABC

, suppose we have

a> b

, where

a=BC

and

b=AC

. Let

M

be the midpoint of

AB

, and

\alpha, \beta

are inscircles of the triangles

ACM

and

A'B'=\frac{a - b}{2}

respectively. Let then

A'

and

B'

be the points of tangency of

\alpha

and

\beta

on

CM

. Prove that

A'B'=\frac{a - b}{2}

.

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