MathDB

CX is angle bisector of <ACB if C,X,Y are collinear, touchpoints of incircle

Source: Belarus TST 2015 1.3

June 9, 2020

geometryangle bisectorincircle

Problem Statement

The incircle of the triangle

ABC

touches the sides

AC

and

BC

at points

P

and

Q

respectively.

N

and

M

are the midpoints of

AC

and

BC

respectively. Let

X=AM\cap BP, Y=BN\cap AQ

. Given

C,X,Y

are collinear, prove that

CX

is the angle bisector of the angle

ACB

.
I. Gorodnin