Class 10 Mathematics • Sample Paper Set 7

If the angle between two radii of a circle is $130^\circ$, the angle between the tangents at the ends of the radii is:

The length of the tangent from a point A at a distance of 5 cm from the centre of the circle is 4 cm. The radius of the circle is:

Area of a sector of angle $p$ (in degrees) of a circle with radius $R$ is:

If the perimeter and the area of a circle are numerically equal, then the radius of the circle is:

A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q so that $OQ = 12$ cm. Length PQ is:

The area of the circle that can be inscribed in a square of side 6 cm is:

If the circumference of a circle increases from $4\pi$ to $8\pi$, then its area is:

The distance between two parallel tangents to a circle of radius 5 cm is:

The length of the minute hand of a clock is 14 cm. The area swept by the minute hand in 5 minutes is:

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

The area of a quadrant of a circle whose circumference is 22 cm is:

At one end A of a diameter AB of a circle of radius 5 cm, tangent XAY is drawn to the circle. The length of the chord CD parallel to XY and at a distance 8 cm from A is:

If the sum of the areas of two circles with radii $R_1$ and $R_2$ is equal to the area of a circle of radius $R$, then:

In a circle of radius 21 cm, an arc subtends an angle of $60^\circ$ at the centre. The length of the arc is:

A circle can have _____ parallel tangents at the most.

The area of the square that can be inscribed in a circle of radius 8 cm is:

If the angle between two tangents drawn from an external point P to a circle of radius $a$ and centre O is $60^\circ$, then $OP$ is equal to:

The perimeter of a sector of a circle of radius 5.2 cm is 16.4 cm. The area of the sector is:

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

Find the area of a sector of a circle with radius 6 cm if angle of the sector is $60^\circ$.

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.

The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5 minutes.

A quadrilateral ABCD is drawn to circumscribe a circle. Prove that $AB + CD = AD + BC$.

Prove that the parallelogram circumscribing a circle is a rhombus.

A chord of a circle of radius 10 cm subtends a right angle at the centre. Find the area of the corresponding: (i) minor segment (ii) major sector. (Use $\pi = 3.14$)

In the given figure, $XY$ and $X'Y'$ are two parallel tangents to a circle with centre O and another tangent AB with point of contact C intersecting $XY$ at A and $X'Y'$ at B. Prove that $\angle AOB = 90^\circ$.

Find the area of the shaded region in the figure, where ABCD is a square of side 14 cm and APD and BPC are semicircles.

A triangle ABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC into which BC is divided by the point of contact D are of lengths 8 cm and 6 cm respectively. Find the sides AB and AC.

A car has two wipers which do not overlap. Each wiper has a blade of length 25 cm sweeping through an angle of $115^\circ$. Find the total area cleaned at each sweep of the blades.

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

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

A round table cover has six equal designs as shown in the figure. If the radius of the cover is 28 cm, find the cost of making the designs at the rate of Rs 0.35 per cm$^2$. (Use $\sqrt{3} = 1.7$)

A chord of a circle of radius 12 cm subtends an angle of $120^\circ$ at the centre. Find the area of the corresponding segment of the circle. (Use $\pi = 3.14$ and $\sqrt{3} = 1.73$)

Case Study: Ferris Wheel
A Ferris wheel (or a big wheel in the United Kingdom) is an amusement ride consisting of a rotating upright wheel with multiple passenger-carrying components (commonly referred to as passenger cars, cabins, tubs, capsules, gondolas, or pods) attached to the rim in such a way that as the wheel turns, they are kept upright, usually by gravity. A Ferris wheel has a diameter of 50 m and takes 20 minutes to complete one rotation.

Case Study: Rangoli Design
In a rangoli competition, a student made a design using a circle and an equilateral triangle inscribed in it. The radius of the circle is 32 cm.

Case Study: Athletic Track
An athletic track is in the form of a ring whose inner circumference is 352 m, and the outer circumference is 396 m.