In Fig. 10.32, `l` and `m` are two parallel tangents at `A` and `B` . The tangent at `C` makes an intercept `D E` between `l` and `m` . Prove that `/_D F E=90o` .

In fig. l and m are two parallel tangents at A and B. The tangent at C makes an intercept DE between l and m. Find angle DFE .

In a circle, PQ and RS are two parallel tangents at A and B. The tangent at makes an intercept DE between PQ and RS. Then angle DOE is equal to : (where O is centre).

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^(@)

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^@

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 Figure A B C D\ a n d\ A E F D are two parallelograms. Prove that: P E=F Q

In the following figure, If l and m are two tangents and AB is a chord making and angle of 60^@ with the tangent l, then the angle between l and m is __________.

Prove that the intercept of a tangent between two parallel tangents to a circle subtends a right angle at the centre.

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.

In Fig. 10.61, B D C is a tangent to the given circle at point D such that B D=30 c m and C D=7c m . The other tangents B E and C F are drawn respectively from B and C to the circle and meet when produced at A making B A C a right angle triangle. Calculate (i) A F (ii) radius of the circle. (FIGURE)