PQ and RS are two parallel tangents to a circle with centre O and another tangent AB wih point of contact C intersect PQ at A and RS at B. then find `angle AOB`

In Fig XY and X'Y' are two parallel tangents to a circle with centre O and another tangent AB with point of contact C intersecting XY and X'Y' at B , prove that angle AOB = 90^@

In Fig.10.13 , and and are two parallel tangents to a circle with centre O and another tangent AB with point of contact C intersecting contact C intersecting at B.Prove that /_AOB=90^(@)

l and m are two parallel tangents to a circle with centre O,touching the circle at A and B respectively.Another tangent at C intersects the line l at D and m at E.Prove that /_DOE=90^(@).

If PQ and PR be the two tangents to a circle with centre O such that /_QPR=120^(@) then /_POQ is

If Fig , AOB is diameter of a circle with centre O and AC is a tangent to the circle at A . If angle BOC = 130^@ , then find angleACO .

A is a point at a distance 10 cm from the centre O of a circle of radius 6cm . AP and AQ are the tangents to the circle at P and Q .If a tangent BC is drawn at a point R lying on the mirror are PQ to intersect AP at B and AQ at C, find the perimeter of the DeltaABC .

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 ?