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concyclic wanted, midpoints of altitudes in acute related

Source: Switzerland - Swiss MO 2014 p8

July 16, 2020

geometryConcyclicaltitudes

Problem Statement

In the acute-angled triangle

ABC

, let

M

be the midpoint of the atlitude

h_b

through

B

and

N

be the midpoint of the height

h_c

through

C

. Further let

P

be the intersection of

AM

and

h_c

and

Q

be the intersection of

AN

and

h_b

. Show that

M, N, P

and

Q

lie on a circle.