MathDB

Let

ABC

be an acute, scalene triangle, and let

M

N

, and

P

be the midpoints of

\overline{BC}

\overline{CA}

, and

\overline{AB}

, respectively. Let the perpendicular bisectors of

\overline{AB}

and

\overline{AC}

intersect ray

AM

in points

D

and

E

respectively, and let lines

BD

and

CE

intersect in point

F

, inside of triangle

ABC

. Prove that points

A

N

F

, and

P

all lie on one circle.

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