Two tangents `T P` and `T Q` are drawn to a circle with centre `O` from an external point `T` . Prove that `/_P T Q=2/_O P Q` .

Two tangents TP and TQ are drawn to a circle with centre O from an external point T . Prove that /_PTQ=2/_OPQ .

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

Two circles touch externally at a point P From a point T on the tangent at P ,tangents TQ and TR are drawn to the circles with points of contact Q and R respectively.Prove that TQ=TR.( FIGURE )

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.

In the given figure, O is the centre of the circle and TP is the tangent to the circle from an external point T. If /_PBT =30^@ , prove that BA:AT =2:1

In Fig,PQ is a tangent from an external point P to a circle with centre O and OP cuts the circle at T and QOR is a diameter.If /_POR=130^(@) and S is a point on the circle, find /_1+/_2

From any point P tangents of length t_(1) and t_(2) are drawn to two circles with centre A,B and if PN is the perpendicular from P to the radical axis and t_(1)^(2) - t_(2)^(2) = K.PN*AB then K=

If angle between two tangents drawn from a point P to a circle of radius 'a' and the centre O is 90^(@) then prove that OP=sqrt(a)