Two circles touch each other externally at P. AB is a direct common tangent to the two circles, A and B are points of contact and . Then  is

• 35°

• 55°

• 65°

• 65°

The length of the common chord of two intersecting circles is 24 cm. If the diameters of the circles are 30 cm and 26 cm, then the distance between the circles in cm is

• 13

• 14

• 15

• 15

13.

If the radii of two circles be 6 cm and 3 cm and the length of the transverse common tangent be 8 cm, then the distance between the two centres is

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• 
• 
• 

If O is the circumcentre of a triangle ABC lying inside the triangle, then ∠OBC + ∠BAC is equal to

• 90°

• 60°

• 110°

• 80°

ABCD is a cyclic quadrilateral. AB and DC when produced meet at P, If PA = 8 cm, PB = 6 cm, PC = 4 cm, then the length (in cm) of PD is

• 8 cm

• 6 cm

• 10 cm

• 12 cm

A and B are centres of two circles of radii 11 cm and 6 cm, respectively. PQ is a direct common tangent to the circles. If , then length of  will be

• 8.5 cm

• 13 cm

• 12 cm

• 10 cm

A and B are the centres of two circles with radii 11 cm and 6 cm respectively. A common tangent touches these circles at P and Q respectively. If AB  = 13 cm, then the length of PQ is

• 13 cm

• 17 cm

• 8.5 cm

• 12 cm

PT is a tangent to a circle with centre O and radius 6 cm. If PT is 8 cm, then length of OP is

• 10 cm

• 12 cm

• 16 cm

• 16 cm

A circle has its centre at O. A tangent drawn from a point P, which is situated outside the circle, touches the circle at A. If PA= 4 cm and PO = 5 cm, then the length of the radius of the circle is

• 1 cm

• 2 cm

• 3 cm

• 3 cm

If PA and PB are two tangents to a circle with centre O such that ∠APB = 80°, then, ∠AOP = ?

• 40°

• 50°

• ^60°

• 70°