Find the area of the sector of a circle of radius 42 cm and of central angle 30 deg. Also, find the area of the corresponding major sector. [Use pi = 22/7]

Prove that the lengths of tangents drawn from an external point to a circle are equal.

In the given figure, O is the centre of the circle. PQ and PR are tangents. Show that the quadrilateral PQOR is cyclic.

Find the area of the segment AYB shown in the figure, if the radius of the circle is 21 cm and angle AOB = 120 deg . [Use π = 22/7]

Prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact.

From an external point P, two tangents PA and PB are drawn to the circle with centre O. If ∠PAB=50, then find ∠AOB

In the given figure, AC is the diameter of the circle with centre O.

In the given figure, the parallelogram ABCD circumscribe a circle, touching circle at P, Q, R and S.

Two tangents PA and PB are drawn to a circle with centre O from an external point P. Prove that ∠APB= 2(∠OAB)

In Figure, XY and X′Y′ are two parallel tangents to a circle with centre O and another tangent AB with point of contact C

In figure, a circle is inscribed in a Δ ABC having sides BC = 8 cm, AB = 10 cm and AC = 12 cm. Find the length BL, CM, and AN.

In the given figure, Δ ABC is circumscribing a circle. Find the length of BC, if AR = 4 cm, BR = 3 cm and AC = 11 cm.

From an external point P, two tangents PA and PB are drawn to the circle with centre O. Prove that OP is the perpendicular bisector of chord AB.

In the given figure, O is the centre of the circle. If Ð AOB = 145°, then find the value of x.

Prove that the parallelogram circumscribing a circle is a rhombus.

Two concentric circle are of radii 4 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle.

Prove that the lengths of tangents drawn from an external point to a circle are equal.

In the given figure, a circle centered at origin O has radius 7 cm, OC is median of ΔOAB.

The perimeter of a certain sector of a circle of radius 5.6 m is 20.0 m. Find the area of the sector.

A circle is touching the side BC of a A ABC at the point P and touching AB

Find the area of the minor and the major sectors of a circle with radius 6 cm,

If a chord of a circle of radius 10 cm subtends an angle of 60 deg at the centre

The perimeter of a certain sector of a circle of radius 5.6 m is 20.0 m. Find the area of the sector.

In the given figure, diameters AC and BD of the circle intersect at O. If ∠AOB = 60° and OA = 10 cm, then

In the given figure, AB is a diameter of the circle with centre O. AQ, BP and

If a hexagon ABCDEF circumscribes a circle, prove that AB + CD + EF = BC + DE + FA.

A horse, a cow and a goat are tied, each by ropes of length 14 m, at the corners

A circle is inscribed in a right-angled triangle ABC, right-angled at B. If BC = 7 cm and

An arc of a circle of radius 21 cm subtends an angle of 60° at the centre. Find: (i) the length

In figure 1, a right triangle ABC in which ∠B = 90 is shown. Taking AB as diameter, a circle has been drawn

PQRS is a diameter of a circle of radius 6 cm. The lengths PQ, QR and RS are equal. Semi-circles are

Find upto three places of decimal the radius of the circle whose area is the sum of the areas of two

In the given figure, ABC is a triangle in which ∠B = 90, BC = 48 cm and AB = 14 cm.

A quadrilateral ABCD is drawn to circumscribe a circle, as shown in the figure. Prove that AB + CD = AD + BC

In the given figure, tangents PQ and PR are drawn to a circle such that ∠RPQ = 30 .

A pendulum swings through an angle of 30 degree and describes an arc of 8.8 cm in length.

Prove that the tangents drawn at the ends of a diameter of a circle are parallel.

In the given figure, PQ is a chord of the circle centered at O. PT is a tangent to the circle at P.

Two circles with centres O and O’ of radii 6 cm and 8 cm, respectively intersect at two

In the given figure, PT is the tangent to the circle centered at O. OC is Perpendicular to

From an external point, two tangents are drawn to a circle. Prove that the line joining the external point to the centre of the circle bisects the angle between the two tangents.

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

Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line segment joining the points of contacts at the centre.

In the given figure, O is the centre of the circle and QPR is a tangent to it at P. Prove that ∠ QAP + ∠ APR = 90°.

A car has two wipers which do not overlap. Each wiper has a blade of length 21 cm sweeping through an angle of 120°.

In the given figure, O is the centre of the circle. AB and AC are tangents drawn to the circle from point A. If ∠ BAC = 65°, then find the measure of ∠ BOC.

In the given figure, a circle is inscribed in a quadrilateral ABCD in which ∠B = 900. If AD = 17 cm, AB = 20 cm and DS = 3 cm, then find the radius of the circle

Two tangents TP and TQ are drawn to a circle with centre 0 from an external point T. Prove that ∠PTQ = 2∠OPQ