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OXY and HBC are similar (complex moment)

Source: 2022 Thailand Online MO P5

April 4, 2022

geometrysimilar trianglesgeometry solvedThailandThailand online MOAngle Chasingreflection

Problem Statement

Let

ABC

be an acute triangle with circumcenter

O

and orthocenter

H

. Let

M_B

and

M_C

be the midpoints of

AC

and

AB

, respectively. Place points

X

and

Y

on line

BC

such that

\angle HM_BX = \angle HM_CY = 90^{\circ}

. Prove that triangles

OXY

and

HBC

are similar.