MathDB

7 circles related problem, in pairs externally tangent

Source: Switzerland - Swiss TST 2003 p8

February 18, 2020

tangent circlescirclesgeometry

Problem Statement

Let

A_1A_2A_3

be a triangle and

\omega_1

be a circle passing through

A_1

and

A_2

. Suppose that there are circles

\omega_2,...,\omega_7

such that: (a)

\omega_k

passes through

A_k

and

A_{k+1}

for

k = 2,3,...,7

, where

A_i = A_{i+3}

, (b)

\omega_k

and

\omega_{k+1}

are externally tangent for

k = 1,2,...,6

. Prove that

\omega_1 = \omega_7