Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle.

2

(a)

Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.

2

(a)

In figure, \(\Delta ABC\) is circumscribing a circle.Find the length of BC.

2

(a)

In the given figure, RS is the tangent to the circle at L and MN is a diameter. If, determine \(\angle RLM.\)

2

(a)

The two tangents from an external point P to a circle with centre O are PA and PB.If \(\angle APB=70^0\), what is the value of \(\angle AOB ?\)

2

(a)

In figure, two circles touch each other at the point C.Prove that the common tangent to the circles at C, bisects the common tangent at P and Q.

2

(a)

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

2

(a)

Prove that the tangent drawn at the mid-point of an arc of a circle is parallel to the chord joining the end points of the arc

2

(a)

Two circles touch internally at a point P and from a point T the common tangent at P, tangent segments TQ, TR are drawn to the two circles. Prove that TQ = TR.

2

(a)

C(0, r₁) and C(0, r₂) are two concentric circles, with r₁ > r₂.AB is a chord of C(0, r₁) touching C(0, r₂) at C, then the relation between AB, r₁ and r₂.

2

(a)

In the given figure, a circle touches all the four sides of a quadrilateral ABCD, whose sides AB = 8cm, BC = 9 cm and CD = 6 cm. Find AD.

2

(a)

 Angle between two tangents PQ and PR from point P to a circle with centre O, is right angle. If the radius of the circle is 4cm, then find the length of each tangent.

2

(a)

How many tangents can a circle have?

2

(a)

Two parallel lines touch the circle at points A and B separately. If the area of the circle is \(25\pi \ { cm }^{ 2 }\), then find the distance between them.

2

(a)