Question

In Fig. 10.2, AB and CD are two equal chords of a circle with centre O. OP and OQ are perpendiculars on chords AB and CD, respectively. If ∠POQ = 150º, then ∠APQ is equal to

AB and AC are two equal chords of a circle. Prove that the bisector of the angle BAC passes through the centre of the circle.

If two equal chords of a circle intersect, prove that the parts of one chord are separately equal to the parts of the other chord.

Two equal chords AB and CD of a circle when produced intersect at a point P. Prove that PB = PD.