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Geometry with orthocenter I

Source: Philippine Mathematical Olympiad 2024 P3

February 24, 2024

geometryorthocenter

Problem Statement

Given triangle

ABC

with orthocenter

H

, the lines through

B

and

C

perpendicular to

AB

and

AC

, respectively, intersect line

AH

at

X

and

L

, respectively. The circle with diameter

XY

intersects lines

BX

and

CY

a second time at

K

and

L

, respectively. Prove that points

H, K

and

L

are collinear.

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