AC is transverse common tangent to two circles with centres P and Q and radii 6cm and 3 cm at the point A and C, respectively. If AC cuts PQ at the point B and AB = 8 cm, then the length of PQ is

• 10 cm

• 12 cm

• 13 cm

• 13 cm

PR is a tangent to a circle with centre O and radius 4 cm at point Q. If , OR = 5 cm and OP =  then the length of PR is:

• 3 cm

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A chord of a circle is equal to its radius. A tangent is drawn to the circle at an extremity of the chord. The angle between the tangent and the chord is

• 30°

• 45°

• 60°

• 60°

Two circles with centres P and Q touch each other externally. A straight line drawn through the point of contact intersects the circle with centre P at A and the circle with centre Q at B. Then, which of the following is true?

• AP = BQ

• AP/BQ

• AP || BQ

• AP || BQ

PQ is a tangent to the circle at T. If TR = TS where R and S are points on the circle and ∠RST = 65°, the ∠PTS = ?

• 65°

• 130°

• 115°
• 115°

In a circle, a diameter AB and a chord PQ (which is not a diameter) intersect each other at X perpendicularly. If AX : BX = 3 : 2 and the radius of the circle is 5 cm, then the length of chord PQ is

7.

Let P and Q be two points on a circle with centre O. If two tangents of the circle through P and Q meet at A with  is

• 96° 

• 48° 

• 66° 

• 66° 

AB is a diameter of a circle with centre O. The tangents at C meets AB produced at Q. If , then measure of  is

• 56° 

• 34° 

• 68° 

• 68° 

The radius of a circle is 6 cm. The distance of a point lying outside the circle from the centre is 10 cm. The length of the tangent drawn from the outside point to the circle is

• 5 cm

• 6 cm

• 7 cm

• 8 cm

A, B, C are three points on a circle. The tangent at A meets BC produced at T, . The angle subtended by BC at the centre of the circle is

• 84°

• 92°

• 96°

• 96°