Question

if the perpendicular bisector of a chord AB of a circle PXAQBY intersects the circle at P and Q, prove that arc PXA is congruent to arc PYB

Answer 1

PAB is an isosceles triangle, because,  PA = PB ,  (P is on perpendicular bisector).  Hence, angle PAB = angle PBA.

If two arcs subtend equal angles at points on the circumference, then the arcs must be equal.  Here arcs PYB & PXA subtend angle PAB = angle PBA.

proved.

Answer 2

hope this will help u.....