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concyclic, BM=BC,AN=AC, BP=BN, AQ=AM (2015 From Tasks to Tasks, p14 Ukr)

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May 3, 2021

geometryConcyclicequal segments

Problem Statement

On the side

AB

of the triangle

ABC

mark the points

M

and

N

, such that

BM = BC

and

AN = AC

. Then on the sides

BC

and

AC

mark the points

P

and

Q

, respectively, such that

BP = BN

and

AQ = AM

. Prove that the points

C, Q, M, N

and

P

lie on the same circle.

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