P is a point on a circle with centre 0. If P is equidistant from the two radii OA and OB, prove that arc `AP = arc BP`.

AP and AQ are two tangents drawn from an external point A to a circle with centre O, P and Q are points of contact. If PR is a diameter, prove that OA||RQ.

Two equal chord AB and CD of a circle with centre O, intersect each other at point P inside the circle. Prove that: BP = DP

In a circle with centre P, AB is a minor arc. Point Ris a point other than A and B on major arc AB. If angle ARB = 80^(@), then angle APB= ........

In a circle with centre P, AB is a minor arc. Point Ris a point other than A and B on major arc AB. If angle ARB = 80^(@), then angle APB= ........

If the perpendicular bisector of a chord AB of a circle PXAQBY intersects the circle at P and Q, prove that arc PXA cong"arc "PYB .

If the perpendicular bisector of a chord AB of a circle PXAQBY intersects the circle at P and Q, prove that arc PXA cong"arc "PYB .

In a circle with centre P, AB is a minor arc. Point Ris a point other than A and B on major arc if ANGLE /_APB = 150^(@). then angle ARB= .........

In a circle with centre P, AB is a minor arc. Point Ris a point other than A and B on major arc iF ANGLE apb = 150^(@). then angle ARB= .........