MathDB

proving tangency and collinearity

Source: IGO 2021 Advanced P3

December 30, 2021

geometryIGOigo p3

Problem Statement

Consider a triangle

ABC

with altitudes

AD, BE

, and

CF

, and orthocenter

H

. Let the perpendicular line from

H

to

EF

intersects

EF, AB

and

AC

at

H

and

L

, respectively. Point

K

lies on the side

BC

such that

BD=KC

. Let

\omega

be a circle that passes through

H

and

P

, that is tangent to

AH

. Prove that circumcircle of triangle

ATL

and

\omega

are tangent, and

KH

passes through the tangency point.

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