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Let the Nagel point of triangle

ABC

N

. We draw lines from

B

and

C

N

so that these lines intersect sides

AC

and

AB

D

and

E

respectively.

M

and

T

are midpoints of segments

BE

and

CD

respectively.

P

is the second intersection point of circumcircles of triangles

BEN

and

CDN

l_1

and

l_2

are perpendicular lines to

PM

and

PT

in points

M

and

T

respectively. Prove that lines

l_1

and

l_2

intersect on the circumcircle of triangle

ABC

.
Proposed by Nima Hamidi

Problem Statement