MathDB

common tangent to unequal circles inscribed in equal consecutive angles

Source: Sharygin 2010 Final 8.4

October 2, 2018

geometrytangentcirclesequal anglescommon tangents

Problem Statement

Circles

\omega_1

and

\omega_2

inscribed into equal angles

X_1OY

and

Y OX_2

touch lines

OX_1

and

OX_2

at points

A_1

and

A_2

respectively. Also they touch

OY

at points

B_1

and

B_2

. Let

C_1

be the second common point of

A_1B_2

and

\omega_1, C_2

be the second common point of

A_2B_1

and

\omega_2

. Prove that

C_1C_2

is the common tangent of two circles.