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3 right angles given, 4 points concyclic wanted

Source: 1986 Polish MO Finals p6

January 21, 2020

geometryConcycliccyclic quadrilateralperpendicularaltitude

Problem Statement

ABC

is a triangle. The feet of the perpendiculars from

B

and

C

to the angle bisector at

A

are

K, L

respectively.

N

is the midpoint of

BC

, and

AM

is an altitude. Show that

K,L,N,M

are concyclic.