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centers of 4 circles are vertices of a rectangle

Source: Mexican Mathematical Olympiad 1989 OMM P5

July 27, 2018

geometryrectangletangent circles

Problem Statement

Let

C_1

and

C_2

be two tangent unit circles inside a circle

C

of radius

2

. Circle

C_3

inside

C

is tangent to the circles

C,C_1,C_2

, and circle

C_4

inside

C

is tangent to

C,C_1,C_3

. Prove that the centers of

C,C_1,C_3

and

C_4

are vertices of a rectangle.

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