MathDB

AN = ID wanted, incenter and incircle of right triangle

Source: OLCOMA Costa Rica National Olympiad, Final Round, 2015 Shortlist G1 day2

September 30, 2021

geometryincenterright triangle

Problem Statement

Consider

\vartriangle ABC

, right at

B

, let

I

be its incenter and

F,D,E

the points where the circle inscribed on sides AB,

BC

and

AC

, respectively. If

M

is the intersection point of

CI

and

EF

, and

N

is the intersection point of

DM

and

AB

. Prove that

AN = ID