O is an centre of a circle. P is an external point of it at distance of 13 cm from O. The radius of the circle is 5 cm. Then the length of a tangent to the circle P upto the point of contact is

• √194 cm

• 10 cm

• 12 cm

• 8 cm

O is a centre of a circle and AB is the tangent to it touch at B. If OB = 3 cm and OA = 5 cm, then the measure of AB (in cm) is

• √34

• 2

• 8

• 4

If PQ and PR be the two tangents to a circle with centre O such that ∠QPR = 120°, then ∠POQ is

• 90°

• 45°

• 30°

• 60°

PQ is a direct common tangent of two circles of radii r₁ and r₂ touching each other externally at A. Then, the value of PQ² is

• r₁r₂

• 2r₁r₂

• 3r₁r₂

• 4r₁r₂

The tangents drawn at the points A and B of a circle centred at O meet at P. If  then  is

• 3 : 2

• 4 : 1

• 2 : 1

• 2 : 5

If the length of a chord of a circle, which makes an angle 45° with the tangent drawn at one end point of the chord, is 6 cm, then the radius of the circle is

• 5 cm

• 3√2 cm

• 6 cm

• 6√2 cm

From a point P which is at a distance of 13 cm from centre O of a circle of radius 5 cm, in the same plane, a pair of tangents PQ and PR are drawn to the circle. Area of quadrilateral PQOR is

• 65 cm²

• 60 cm²

• 30 cm²

• 90 cm²

A tangent is drawn to a circle of radius 6 cm from a point situated at a distance of 10 cm from the centre of the circle. The length of the tangent will be

• 7 cm

• 4 cm

• 8 cm

• 5 cm

In the given figure,  and MN is a tangent at R. What is the value (in degrees) of x,y and z respectively.

• 40°, 46°,  94°

• 40°, 50°,  90°

• 46°, 54°,  80°

• 50°, 40°,  90°

In ΔPQR,  the perpendicular of PQ at S meets QR at T. If  then what is the value (in degrees) of ?

• 25°

• 40°

• 50°

• 60°