In the given figure, ABCD is a cyclic quadrilateral in which CB = CD and TC is a tangent to the circle at C. If O is the centre of the circle and BC is produced to E such that ∠DCE = 110°, find:

(i) ∠DCT

(ii) ∠BOC

In the given figure, AC is a tangent to the circle with centre O. If ∠ADB = 55°, find x and y. Give reasons.

The length of the tangent drawn to a circle of radius 8 cm, from a point which is at a distance of 10 cm from the centre of the circle is :

1. 6 cm

2. 7 cm

3. 9 cm

4. 2 cm

There are two tangents to a circle passing through a point lying outside the circle.

1. at least

2. at most

3. exactly

4. maximum