MathDB

perpendicularity wanted, intersections of tangents with perp. bisectors related

Source: BMO Shortlist 2018 G2

May 5, 2019

geometryperpendicular bisectororthocenterperpendicularperpendicularitytangentcircumcircle

Problem Statement

Let

ABC

be a triangle inscribed in circle

\Gamma

with center

O

. Let

H

be the orthocenter of triangle

ABC

and let

K

be the midpoint of

OH

. Tangent of

\Gamma

B

intersects the perpendicular bisector of

AC

L

. Tangent of

\Gamma

C

intersects the perpendicular bisector of

AB

M

. Prove that

AK

and

LM

are perpendicular.
by Michael Sarantis, Greece