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Two altitudes and two midpoints. 4 noncyclic points are wanted

Source: St. Petersburg MO 2000, 10th grade, P2

April 22, 2023

geometryaltitudesmidpointscyclic quadrilateral

Problem Statement

Let

AA_1

and

BB_1

be the altitudes of acute angled triangle

ABC

. Points

K

and

M

are midpoints of

AB

and

A_1B_1

respectively. Segments

AA_1

and

KM

intersect at point

L

. Prove that points

A

K

L

and

B_1

are noncyclic.
[I]Proposed by S. Berlov