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^@`

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.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^(@).

In Fig , XP and XQ are two tangents to the circle with centre O , drawn from an external point X . ARB is another tangent, touching the circle at R . Prove that XA + AR = XB + BR.

In Fig common tangents AB and CD to two circles with centres O_1 and O_2 intersect at E. Prove that AB = CD.

The common tangents AB and CD to two circles with centres O and O' intersect at E between the centres.Prove that the points O,E and O' are collinear.

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 .