MathDB

concyclic wanted, angle bisectors related

Source: Russian Regional Olympiad 2010 10.3

August 24, 2024

geometryangle bisectorConcyclic

Problem Statement

In triangle

ABC

, the angle bisectors

AD

,

BE

and

CF

are drawn, intersecting at point

I

. The perpendicular bisector of the segment

AD

intersects lines

BE

and

CF

at points

M

and

N

, respectively. Prove that points

A

,

I

,

M

and

N

lie on the same circle.

Back to Problems View on AoPS