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Points C_1, C_2, B, D lie on the same circle [Slovenia 2010]

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November 16, 2010

geometry proposedgeometry

Problem Statement

Let

\mathfrak K_1

and

\mathfrak K_2

be circles centered at

O_1

and

O_2,

respectively, meeting at the points

A

and

B.

Let

p

be the line through the point

A

meeting the circles

\mathfrak K_1

and

\mathfrak K_2

again at

C_1

and

C_1O_1

Assume that

A

lies between

C_1

and

C_2.

Denote the intersection of the lines

C_1O_1

and

C_2O_2

by

D.

Prove that the points

C_1, C_2, B

and

D

lie on the same circle.

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