MathDB

line AI bisects segment XY , XY _|_ IP

Source: 2023 IGO Adcanced P4

January 18, 2024

geometrybisects segment

Problem Statement

Let

ABC

be a triangle with bisectors

BE

and

CF

meet at

I

. Let

D

be the projection of

I

on the

BC

. Let M and

N

be the orthocenters of triangles

AIF

and

AIE

, respectively. Lines

XY \perp IP

and

FN

meet at

P.

Let

X

be the midpoint of

BC

. Let

Y

be the point lying on the line

AD

such that

XY \perp IP

. Prove that line

AI

bisects the segment

XY

.
Proposed by Tran Quang Hung - Vietnam

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