Question 60904
let AB be a chord in the circle
let line XY intersect the chord at P.
let O be the centre of the circle.
OP is perpendicular to AB.
Join OA and OB.
you have 2 right angled triangles OAP and OBP.
Considering the two triangles, we have
OA = OB   radii of the circle and the hypotenuse of the right triangles.
OP is common to the two triangles.
angle OPA = angle OPB =90 degrees. 
therefore the two triangles are congruent.(right angle, hypotenuse and side)
hence AP =PB  (corresponding parts of congruent triangles are equal)
the line OP bisects chord AB.