MathDB

The two circles

{{w} _ {1}}, \, \, {{w} _ {2}}

touch externally at the point

Q

. The common external tangent of these circles is tangent to

{{w} _ {1}}

at the point

B

BA

is the diameter of this circle. A tangent to the circle

{{w} _ {2}}

is drawn through the point

A

, which touches this circle at the point

C

, such that the points

B

and

C

lie in one half-plane relative to the line

AQ

. Prove that the circle

{{w} _ {1}}

bisects the segment

C

.
(Igor Nagel)

Problem Statement