MathDB

concyclic wanted, altitudes and midpoints related

Source: 2014 NZOMC Camp Selections p5

January 10, 2021

geometryConcyclic

Problem Statement

Let

ABC

be an acute angled triangle. Let the altitude from

C

AB

meet

AB

C'

and have midpoint

M

, and let the altitude from

B

AC

meet

AC

B'

and have midpoint

N

. Let

P

be the point of intersection of

AM

and

BB'

and

Q

the point of intersection of

AN

and

CC'

. Prove that the point

M, N, P

and

Q

lie on a circle.