MathDB

Let

ABC

be a triangle with

AB = AC

. The incircle touches

BC

AC

and

AB

D

E

and

F

respectively. Let

P

be a point on the arc \overarc{EF} that does not contain

D

. Let

Q

be the second point of intersection of

BP

and the incircle of

ABC

. The lines

EP

and

EQ

meet the line

BC

M

and

N

, respectively. Prove that the four points

P, F, B, M

lie on a circle and

\frac{EM}{EN} = \frac{BF}{BP}

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