Two tangent segments PA and PB are drawn to a circle with centre O such that `angleAPB=120^@`. Prove that OP=2AP.

Two tangent TP and TQ are drawn to a circle with centre O from an external point T. prove that angle PTQ=2 angle OPQ.

From an external point P, tangent PA=PB are drawn to a circle with centre O. If anglePAB=50^@, then find angleAOB .

In the given figure. If TP and TQ are the two tangents to a circle with centre O so that angle POQ= 110^(@) , then angle PTQ is equal to …….

AB is a diameter and AC is a chord of a circle with centre O such that angleBAC=30^@ . The tangent at C intersects AB at a point D. Prove that BC=BD.

If tangent PA and PB from point P to a circle with centre O are inclided to each other at an angle of 80^(@) . Then anglePOA = ……..

Choose the correct answer and give justification for each. If tangents PA and PB from a point P to a circle with centre O are inclined to each other at angle of 80^(@) , then /_POA is equal to

Two tangents TA and TB to circle with centre O are inclined to each other angle of 70^(@) . Then, Find angleOAB .

Choose the correct answer and give justification for each. If AP and AQ are the two tangents a circle with centre O so that /_POQ=110^(@) , then /_PAQ is equal to

Two circles intersect at two points B and c. Through B, two line segments ABD and PBQ are drawn to intersect the circles at A, D and P, Q respectively (see the given figure). Prove that angle ACP = angle QCD.