Let us fill in the blanks.

(i) If a straight line intersects the circles at two points, then the straight line is called ______of circle.

(ii) If two circles do not intersect or touch each other, then the maximum number of common tangents can be drawn is ________.

(iii) Two circles touch each other externally at the point A. A common tangent drawn to two circles at the point A is _______ common tangent (direct/transverse)

The lengths of radii of two circles are 3.5 cm and 2 cm. The two circles touch each other internally. The distances between the centre of two circles is

Let us write whether the following statements are true of false:

(i) P is a point inside a circle. Any tangent drawn on the circle does not pass through the point P.

(ii) There are more than two tangents can be drawn to a circle parallel to a fixed line.

In the adjoining figure O is the centre and BOA is a diameter of the circle. A tangent drawn to a circle at the point P intersects the extended BA at the point T. If ∠PBO = 30°, let us find the value of ∠PTA.

In the adjoining figure, ΔABC circumscribed a circle and touches the points P,Q,R. If AP = 4 cm, BP = 6cm, AC = 12 cm and BC = x cm, let us determine the value of x.