If from an external point P of a circle with centre O, two tangents PQ and PR are drawn such `/_QPR=120^@`, prove that 2PQ=PO.

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.

In Fig. two tangents RQ and RP are drawn from an external point R to the circle with centre O. If anglePRQ = 120 ^@ , then prove that OR = PR + RQ .

AP and AQ are two tangents drawn from an external point A to a circle with centre O, P and Q are points of contact. If PR is a diameter, prove that OA||RQ.

PQ is a tangent drawn from an external point P to a circle with center O, angle QOR is the diameter of the circle. If angle POR = 120^(@) . What is the measure of angle OPQ ?

PR and PS are two tangents drawn from a extental point P of the Circle with centre at O. If PR =8 cm and angle RPO=60^(@), then the length of PS=

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.

In the figure , PQ and PR are tangents drawn from and external point P to the circle with centre O. Q and R are the points of contact. If PQ = 5 cm then what is the length of segment PR ? Why ?