MathDB

In the circumscircle of a triangle

ABC

, let

A_1

be the point diametrically opposed to the vertex

A

. Let

A'

the intersection point of

AA'

and

BC

. The perpendicular to the line

AA'

from

A'

meets the sides

AB

and

AC

M

and

N

, respectively. Prove that the points

A,M,A_1

and

N

lie on a circle which has the center on the height from

A

of the triangle

ABC

Problem Statement