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Prove that the lines KH and CD are perpendicular

Source: Moldova TST 2021

September 20, 2021

geometry

Problem Statement

In a convex quadrilateral

ABCD

the angles

BAD

and

BCD

are equal. Points

M

and

N

lie on the sides

(AB)

and

(BC)

such that the lines

MN

and

AD

are parallel and

CD

. The point

H

is the orthocenter of the triangle

ABC

and the point

K

is the midpoint of

MN

. Prove that the lines

KH

and

CD

are perpendicular.

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