AB and CD are two equal chords of a circle which is intersecting at P as shown in fig. P is joined to O, the center of the circle. So we need to Prove that OP bisects

Construction: In the given figure draw perpendiculars OM and ON to AB and CD respectively.

Now, we have to consider the and ,

OP = OP … [common side for both triangles of the given figure]

OM = ON … [distance of equal chords from the center of circle are equal]

… [both the angles are equal that is ]

Therefore, we can say that

So,

Hence we have proved that, OP bisects .