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CT bisects MP, AM=AN,BM=BK, circumcircle related (Kharkiv City X 2018- Ukr)

Source:

March 21, 2020

geometrycircumcircleKharkivequal segmentsbisects segment

Problem Statement

On the sides

AB, AC ,BC

of the triangle

ABC

, the points

M, N, K

are selected, respectively, such that

AM = AN

and

BM = BK

. The circle circumscribed around the triangle

MNK

intersects the segments

AB

and

BC

for the second time at points

P

and

Q

, respectively. Lines

MN

and

PQ

intersect at point

T

. Prove that the line

CT

bisects the segment

MP