In the figure `PO _|_ QO`. The tangents to the circle at P and Q intersect at a point T. Prove that PQ and OT are right bisectors of each other.

If two circles intersect at two points, prove that their centres lie on the perpendicular bisector of the common chord.

If two circles intersect at two points, prove that their centres lie on the perpendicular bisector of the common chord.

In the given figure, AB, BC and Ac are tangents to the circle at P,Q and R. If AB = AC, show that Q is the mid-point of BC.

In the figure, PQL and PRM are tangents to the circle with centre O at the points Q and R respectively and S is a point on the circle such that |__SQL=50^(@) and |__SRM=60^(@) . Find |__QSR .

In the given figure, two circles touch each other externally at the point C. Prove that the common tangent to the circle at C bisects the common tangents at P and Q.

In the figure, PQ is a chord of length 8 cm of a circle of radius 5 cm. The tangents at P and Q intersect at T. Find TP and TQ.

In the figure, O is the centre of a circle of radius 5 cm. T is the point such that OT=13cm and OT intersects the circle at E. If AB is the tangent to the circle at E, find the length of AB.

In the given figure PQ & RS are two parallel tangents to a circle o and another tangent AB with point of contact C intersecting PQ at A and RS at B. Prove that angleAOB = 90^@

In Fig . two chords AB and CD intersect each other at the point P. prove that : AP.PB=CP.DP

In Fig . two chords AB and CD intersect each other at the point P. prove that : DeltaAPC~DeltaDPB