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Intersecting circles

Source: Indonesia Mathematics Olympiad 2004 Day 1 Problem 4

October 22, 2009

Problem Statement

There exists 4 circles,

a,b,c,d

, such that

a

is tangent to both

b

and

d

b

is tangent to both

a

and

c

c

is both tangent to

b

and

d

, and

d

is both tangent to

a

and

c

. Show that all these tangent points are located on a circle.