MathDB

right angle wanted, excirle and incircle related

Source: OLCOMA Costa Rica National Olympiad, Final Round, 2014 4.5

September 24, 2021

geometryexcircleincircleright angle

Problem Statement

Let

ABC

be a triangle, with

A'

B'

, and

C'

the points of tangency of the incircle with

BC

CA

, and

AB

respectively. Let

X

be the intersection of the excircle with respect to

A

with

AB

, and

M

the midpoint of

BC

. Let

D

be the intersection of

XM

with

B'C'

. Show that

\angle C'A'D' = 90^o