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concyclic wanted, 2 circumcircles related

Source: 2017 NZOMC Camp Selections p6

January 10, 2021

geometryConcyclic

Problem Statement

Let

ABCD

be a quadrilateral. The circumcircle of the triangle

ABC

intersects the sides

CD

and

DA

in the points

P

and

Q

respectively, while the circumcircle of

CDA

intersects the sides

AB

and

BC

in the points

R

and

S

. The lines

BP

and

BQ

intersect the line

RS

in the points

M

and

N

respectively. Prove that the points

M, N, P

and

Q

lie on the same circle.

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