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parallelogram from intersections, starting with 2 intersecting circles

Source: Rioplatense Olympiad 2011 level 3 P4

September 3, 2018

geometryparallelogramcircles

Problem Statement

We consider

\Gamma_1

and

\Gamma_2

two circles that intersect at points

P

and

Q

. Let

A , B

and

C

be points on the circle

\Gamma_1

and

D , E

and

F

points on the circle

\Gamma_2

so that the lines

N

and

B D

intersect at

P

and the lines

A C

and

D F

intersect at

A M D N

. Denote

M

and

N

the intersections of lines

A B

and

D E

and of lines

A C

and

D F

, respectively. Show that

A M D N

is a parallelogram.

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