A point P lies outside the circle with centre O. two lines PAOB and PDC are drawn on the circle from P. if PD =OD, then prove that arc `BC=3xxArcAD`.

From a point P outside a circle with centre O , tangents PA and PB are drawn to the circle. Prove that OP is the right bisector of the line segment AB .

From a point P outside a circle, with centre O, tangents PA and PB are drawn. Prove that (i) /_AOP=/_BOP (ii) OP is the _|_ bisector of chord AB.

If from an external point B of a circle with centre O, two tangents BC and BD are drawn such that angleDBC=120^(@), prove that BC+BD=BO.

P is a point outside a circle with centre O, and it is 14 cm away from the centre. A secant PAB drawn from P intersects the circle at the points A and B such that PA = 10 cm and PB = 16 cm. The diameter of the Circle is:

PA and PB are two tangents to a circle with centre O, from a point P outside the circle . A and B are point P outside the circle . A and B are point on the circle . If angle PAB = 47^(@) , then angle OAB is equal to :

A point P is 13 cm from the centre of the circle. The two tangent PQ and PR are drawn from the point P, The length of the tangent drawn from P to the circle is 12 cm. Find the radius of the circle.

A point P is 26 cm away from the centre O of a circle and PT is the tangent drawn from P to circle is 10 cm , then OT is equal to ……………