MathDB

Let

ABC

be a triangle with an obtuse angle at

A

. Let

E

and

F

be the intersections of the external bisector of angle

A

with the altitudes of

ABC

through

B

and

C

respectively. Let

M

and

N

be the points on the segments

EC

and

FB

respectively such that

\angle EMA = \angle BCA

and

\angle ANF = \angle ABC

. Prove that the points

E, F, N, M

lie on a circle.

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