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concyclic wanted, altitude and perpendiculars related

Source: Ukraine TST 2015 p6

May 1, 2020

geometryConcyclicperpendicularaltitude

Problem Statement

Given an acute triangle

BC

is the foot of the altitude drawn from the point

A

on the line

BC, P

and

K \ne H

are arbitrary points on the segments

AH

and

BC

respectively. Segments

AC

and

BP

intersect at point

B_1

, lines

AB

and

CP

at point

C_1

. Let

X

and

Y

be the projections of point

H

on the lines

KB_1

and

KC_1

, respectively. Prove that points

A, P, X

and

Y

lie on one circle.

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