In Figure, ` hat A B~= hat A C` and `O` is the centre of the circle. Prove that `O A` is the perpendicular bisector of `B C`

In Figure, A B=C B\ a n d\ O is the centre of the circle. Prove that B O bisects /_A B C .

From an external point P , two tangents PA and PB are drawn to the circle with centre O . Prove that O P is the perpendicular bisector of A B .

In Figure, O is the centre of the circle. Find /_B A C

In Figure, O is the centre of the circle. Find /_C B D

In Figure, O is the centre of a circle and P O BISECTS /_A P D . Prove that A B=C D

In Figure, it is given that O is the centre of the circle and /_A O C=150^@ . Find /_A B C

In Figure, A B C D is a cyclic quadrilateral; O is the centre of the circle. If /_B O D=160^0, find the measure of /_B P D

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

Let C be the mid-point of an arc A B of a circle such that m\ hat A B=183^0dot If the region bounded by the arc A C B and line segment A B is denoted by S , then the centre O of the circle lies (a) in the interior of S (b) in the exterior of S on the segment A B (d) on A B and bisects A B