MathDB

Suppose

ABCD

is a parallelogram. Consider circles

w_1

and

w_2

such that

w_1

is tangent to segments

AB

and

AD

and

w_2

is tangent to segments

BC

and

CD

. Suppose that there exists a circle which is tangent to lines

AD

and

DC

and externally tangent to

w_1

and

w_2

. Prove that there exists a circle which is tangent to lines

AB

and

BC

and also externally tangent to circles

w_1

and

w_2

.
Proposed by Ali Khezeli

Problem Statement