Question

Two equal circle touch externally at point P. PX and PY are chords in the respective circles which are perpendicular. If the centres Are A and B. Show that AX is parallel to BY and AXYB is a parallelogram.

Answer 1

Draw the diameters through A and B and P. The Draw lines connecting X and Y to the ends opposite P. Now you have two congruent right triangles. The rest follows pretty easily.