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4 circles, externally tangent in pairs

Source: Mexican Mathematical Olympiad 2000 OMM P1

July 28, 2018

geometrytangent circles

Problem Statement

Circles

A,B,C,D

are given on the plane such that circles

A

and

B

are externally tangent at

P, B

and

C

at

Q, C

and

D

at

R

, and

D

and

A

at

S

. Circles

A

and

C

do not meet, and so do not

B

and

D

. (a) Prove that the points

P,Q,R,S

lie on a circle. (b) Suppose that

A

and

C

have radius

2, B

and

D

have radius

3

, and the distance between the centers of

A

and

C

is

6

. Compute the area of the quadrilateral

PQRS

.

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