Two chords AB and CD intersect at P inside the circle . Prove that the sum of the angles substended by the arcs AC and BD at the centre O is equal to twice the angle APC.

If the angles subtended by two chords of a circle at the centre are equal, then Prove chords are equal.

The chord of a circle is equal to its radius, find the angle subtended by this chord at the centre.

Prove that equal chords of congruent circles subtend equal angles at their centre.

Prove that equal chords of congruent circles subtend equal angles at their centre.

Let the vertex of an angle ABC be located outside a circle and let the sides of the angle intersect equal chords AD and CE with the circle. Prove that \ /_A B C is equal to half the difference of the angles subtended by the chords AC and DE at the centre.

Let the vertex of an angle ABC be located outside a circle and let the sides of the angle intersect equal chords AD and CE with the circle. Prove that \ /_A B C is equal to half the difference of the angles subtended by the chords AC and DE at the centre.

If two equal chords of a circle intersect within the circle, prove that the line joining the point of intersection to the centre makes equal angles with the chords.

Two chords A B and A C of a circle are equal. Prove that the centre of the circle lies on the angle bisector of /_B A Cdot

Two chords A B and A C of a circle are equal. Prove that the centre of the circle lies on the angle bisector of /_B A Cdot

If chords AB and CD of a circle intersect each other at a point inside the circle, prove that : PA xx PB = PC xx PD .