I saw a theorem (which is true):
Let $P$ and $Q$ be the centers of two tangent circles. Draw a line from a point through the intersection of the two circles and let that line intersect the circles at $B$ and $C$. Then $BP$ is parallel to $CQ$.
Angles BAP and CAQ are vertical and hence equal. Triangles BAP and CAQ are isosceles with equal base angles at A. The other pair of the base angles are also equal. I.e., ∠ABP = ∠ ACQ. These two angles are internal to the lines BP and CQ and transversal BC. Since the internal angles are equal, the lines are parallel: PB || QC. (Source: here)
What can I say about the converse? i.e. if $PB || QC$ then the circles are tangent. Is that true?
I appreciate all help.