MathDB

circumcenter of ABN is midpoint of incenter's segment of ABC and ABM

Source: Czech-Polish-Slovak Junior Match 2016, team p5 CPSJ

January 20, 2020

geometryincenterCircumcentermidpoint

Problem Statement

Let

ABC

be a triangle with

AB : AC : BC =5:5:6

. Denote by

M

the midpoint of

BC

and by

N

the point on the segment

BC

such that

BN = 5 \cdot CN

. Prove that the circumcenter of triangle

ABN

is the midpoint of the segment connecting the incenters of triangles

ABC

and

ABM

.
Slovakia