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externally tangent circles in pairs , diameter wanted

Source: Cono Sur Shortlist 2003 G2

July 26, 2019

tangent circlesdiametergeometry

Problem Statement

The circles

C_1, C_2

and

C_3

are externally tangent in pairs (each tangent to other two externally). Let

M

the common point of

C_1

and

C_2, N

the common point of

C_2

and

C_3

and

P

the common point of

C_3

and

C_1

. Let

A

be an arbitrary point of

C_1

. Line

AM

cuts

C_2

in

B

, line

BN

cuts

C_3

in

C

and line

CP

cuts

C_1

in

D

. Prove that

AD

is diameter of

C_1

.

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