The two circles w1,w2 touch externally at the point Q. The common external tangent of these circles is tangent to w1 at the point B, BA is the diameter of this circle. A tangent to the circle w2 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 w1 bisects the segment C.(Igor Nagel) bisects segmentcirclestangent circlesgeometry