Two straight lines OAB and OCD are drawn from an external point O to cut a given circle at A, B, C, D. Prove that the intersection of AD and BC cannot be the centre of the circle.

Two tangents PQ and PR are drawn from an external point to a circle with centre O . Prove that QORP is cyclic quadrilateral.

In the adjoining figure, two tangents drawn from external point C to a circle with centre O touches the circel at the point P and Q respectively. A tangent drawn at another point R of the circle intersects CP and CQ at the points A and B respectively. If CP = 7 cm and BC =11 cm, then determine the length of BR.

Two tangents are drawn from an external point A of the circle with centre at O which touches the circle at the points B and C. Prove that AO is the perpendicular bisector of BC.

Two tangents AB and AC drawn from an external point A of a circle touch the circle at the point B and C .A tangent drawn a point X lies on minor are BC intersects AB and AC at the points D and E respectively. Prove that perimeter of DeltaADE=2AB.

Two tangents AB and AC drawn from an external point A of a circle touch the circle at the point B and C. A tangent drawn to a point X lies on minor arc BC intersects AB and AC at the points D and E respectively. Prove that peremeter of triangleADE = 2AB .

Two tangents PA and PB are drawn to a circle with centre O from an external point P. Prove that angle APB = 2 angle OAB

Prove that the internal angle between two tangents drawn from an external point is bisected by the straight line obtained by joining that point and the centre of the circle.

From an external point P, two tangents PAandPB are drawn to the circle with centre O .Prove that OP is the perpendicular bisector of AB.

TA and TB are tangents to a circle with centre O from an external point T. OT intersects the circle at point P. Prove that AP bisects the angle TAB.

PA and PB are two tangents drawn from an external point P at the points A and B on a circle with centre O.If another tangent to the circle intersects PA and PB at L and M respectively,show that LM=AL+BM.