Two parallel lines meet each other at some point.

Two circles intersect each other at the points P and Q. Two straight lines through P and Q intersect one circle at the points A and C and the other circle at B and D. Prove the AC|| BD

Two circles itnersect each other in two points. Prove that the line through their centres is the perpendicular bisector of the common chord.

If a transversal intersects two parallel lines; then each of alternate interior angles are equAL.

In the figure, two circles intersect each other at points A and B. AP and AQ are the diameters of these circels. Prove that PBQ is a straight line.