Choose the correct answer and give justification for each.

If AP and AQ are the two tangents a circle with centre O so that ∠POQ = 110°, then ∠PAQ is equal to



A. 60^o

B. 70^o

C. 80^o

D. 90^o

Choose the correct answer and give justification for each.

From a point Q, the length of the tangent to a circle is 24 cm. and the distance of Q from the centre is 25 cm. The radius of the circle is

A. 7 cm

B. 12 cm

C. 15 cm

D. 24.5 cm

Choose the correct answer and give justification for each.

In the figure XY and X¹Y¹ are two parallel tangents to a circle with centre O and another tangent AB with point of contact C intersecting XY at A and X¹Y¹ at B then ∠AOB =

A. 80^o

B. 100^o

C. 90^o

D. 60^o

Choose the correct answer and give justification for each.

If AP and AQ are the two tangents a circle with centre O so that ∠POQ = 110°, then ∠PAQ is equal to

A. 60^o

B. 70^o

C. 80^o

D. 90^o

Draw a tangent to a given circle with center O from a point ‘R’ outside the circle. How many tangent can be drawn to the circle from that point?

Hint : The distance of two points to the point of contact is the same.

Choose the correct answer and give justification for each.

The angle between a tangent to a circle and the radius drawn at the point of contact is

A. 60^o

B. 30^o

C. 45^o

D. 90^o

Prove that the tangents to a circle at the end points of a diameter are parallel.

In a right triangle ABC, a circle with a side AB as diameter is drawn to intersect the hypotenuse AC in P. Prove that the tangent to the circle at P bisects the side BC.

Draw a circle with the help of a bangle, Take a point outside the circle. Construct the pair of tangents from this point to the circle measure them. Write conclusion.

Choose the correct answer and give justification for each.

If tangents PA and PB from a point P to a circle with centre O are inclined to each other at angle of 80^o, then ∠POA is equal to

A. 50^o

B. 60^o

C. 70^o

D. 80^o