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3 tangent circles in pairs, tangent int. to a 4th Puerto Rico TST 2021.5

Source:

September 22, 2021

tangent circlesgeometry

Problem Statement

Circle

o

contains the circles

m

p

and

r

, such that they are tangent to

o

internally and any two of them are tangent between themselves. The radii of the circles

m

and

p

are equal to

x

. The circle

r

has radius

1

and passes through the center of the circle

o

. Find the value of

x