CBSE Class 10 Mathematics Circles Worksheet Set 08

Circles

Q.- In the given figure, the measure of OQP is 

a. 90°

b. 40°

c. 60°

d. 35°

Q.- In figure, AB is a chord of a circle and AT is a tangent at A such that ,∠BAT=60⁰ measure ∠ACB of is : 

a. 120°

b. 150°

c. 90°

d. 110°

Question. What is the distance between two parallel tangents of a circle of the radius 4 cm.?
Answer: 8 cm

Question. The length of tangent from point A at a distance at 5 cm. from the centre of the circle is 4 cm. What will be the radius of the circle?
Answer: 3 cm

Question. How many tangents can be drawn to a circle from a point inside the circle.
Answer: None

Question. How many tangents can be drawn to a circle from a point outside the circle?
Answer: Two

Question. If O is the centre of two concentric circles of radius 5 cm. and 13 cm. if AB is chord of larger circle which touches the smaller circle. Find the length of chord AB.
Answer: 24 cm

AREAS RELATED TO CIRCLES SECTION A: (1 MARK)

1.If area of a circle is numerically double its perimeter, then find the radius of the circle. (CBSE 2011)(4 units)

2.If the area of a sector is 5/18 of the area of the circle, find the angle subtended by the sector at the centre.(100:)

3.If the diameter of a semicircular protractor is 14 cm, then find its perimeter. (CBSE 2009)(36 cm)

SECTION B: (2 MARKS)

4.A square is inscribed in a circle. What is the ratio of the areas of the circle and the square.(π : 2)

5.The area enclosed between the two concentric circles is 346.5 cm². The circumference of the inner circle is 88 cm. Find the radius of the outer circle. (CBSE 2011)(17.5 cm)

6.Find the number of revolutions made by a circular wheel of area 1.54 cm2 in rolling a distance of 176 cm. (CBSE 2013)(40)

7.If r and R are the respective radii of the smaller and bigger semi-circles, find the area of the shaded portion. ( CBSE 2010)(πR²)

SECTION C: (3 MARKS)

8.The long and short hands of a clock are 6 cm and 4 cm long respectively. Find the sum of the distances travelled by their tips in 24 hours. (Use π = 3.14)(954.56cm)

9.OABC is a rhombus whose three vertices A, B and C lie on a circle with centre O. Find the area of the rhombus, if the area of the circle is 1256 cm2. (Use π = 3.14)(20000√3cm²)

10.ABCD is a field in the shape of a trapezium with AD ‖ BC, ABC = 90: and ADC = 60:. Four sectors are formed with centres A, B, C and D. The radius at each sector is 14 m. Find the total area of four sectors. (CBSE 2012)

11.A steel wire when bent in the form of a square encloses an area of 121 sq. cm. If the same wire is bent into the form of a circle, find the area of the circle.(154 cm²)

SECTION D: (4 MARKS)

12.The diameters of front and rear wheels of a tractor are 80 cm and 2 m respectively. Find the number of revolutions that rear wheel will make in covering a distance in which the front wheel makes 1400 revolutions. (CBSE 2013)(280)

13.Find the area of the shaded region for figure 1.{(180-8π) cm²)}

14.Find the area of shaded region in fig.2, where a circle of radius 6 cm has been drawn with vertex O of an equilateral triangle OAB of side 12 cm.(Use π = 3.14 and 3=1.73) (EXAMPLAR QUESTION)(317.64cm²)

Fig.1

Fig.2

15.In fig.3, ΔABC is right angled at A. Semicircles are drawn on AB, AC and BC as diameters. Find the area of shaded region. (CBSE 2014)

SECTION A: (1 MARK)

Question. If area of a circle is numerically double its perimeter, then find the radius of the circle.
Answer: 4 units

Question. If the area of a sector is \(\frac{5}{18}\) of the area of the circle, find the angle subtended by the sector at the centre.
Answer: \(100^\circ\)

Question. If the diameter of a semicircular protractor is \(14\text{ cm}\), then find its perimeter.
Answer: \(36\text{ cm}\)

SECTION B: (2 MARKS)

Question. A square is inscribed in a circle. What is the ratio of the areas of the circle and the square?
Answer: \(\pi : 2\)

Question. The area enclosed between the two concentric circles is \(346.5\text{ cm}^2\). The circumference of the inner circle is \(88\text{ cm}\). Find the radius of the outer circle.
Answer: \(17.5\text{ cm}\)

Question. Find the number of revolutions made by a circular wheel of area \(1.54\text{ cm}^2\) in rolling a distance of \(176\text{ cm}\).
Answer: 40

Question. If \(r\) and \(R\) are the respective radii of the smaller and bigger semi-circles, find the area of the shaded portion.

Answer: \(\pi R^2\)

SECTION C: (3 MARKS)

Question. The long and short hands of a clock are \(6\text{ cm}\) and \(4\text{ cm}\) long respectively. Find the sum of the distances travelled by their tips in \(24\) hours. (Use \(\pi = 3.14\))
Answer: \(954.56\text{ cm}\)

Question. OABC is a rhombus whose three vertices \(A\), \(B\) and \(C\) lie on a circle with centre \(O\). Find the area of the rhombus, if the area of the circle is \(1256\text{ cm}^2\). (Use \(\pi = 3.14\))
Answer: \(200\sqrt{3}\text{ cm}^2\)

Question. ABCD is a field in the shape of a trapezium with \(AD \parallel BC\), \(\angle ABC = 90^\circ\) and \(\angle ADC = 60^\circ\). Four sectors are formed with centres \(A\), \(B\), \(C\) and \(D\). The radius at each sector is \(14\text{ m}\). Find the total area of four sectors.
Answer: \(616\text{ m}^2\)

Question. A steel wire when bent in the form of a square encloses an area of \(121\text{ sq. cm}\). If the same wire is bent into the form of a circle, find the area of the circle.
Answer: \(154\text{ cm}^2\)

SECTION D: (4 MARKS)

Question. The diameters of front and rear wheels of a tractor are \(80\text{ cm}\) and \(2\text{ m}\) respectively. Find the number of revolutions that rear wheel will make in covering a distance in which the front wheel makes \(1400\) revolutions.
Answer: \(560\) revolutions. (Note: If the radius of the rear wheel is \(2\text{ m}\) instead of the diameter, the answer is \(280\) revolutions).

Question. Find the area of the shaded region for figure 1.
Answer: \((180-8\pi)\text{ cm}^2\)

Question. Find the area of shaded region in fig.2, where a circle of radius \(6\text{ cm}\) has been drawn with vertex \(O\) of an equilateral triangle \(OAB\) of side \(12\text{ cm}\). (Use \(\pi = 3.14\) and \(\sqrt{3} = 1.73\))

Answer: \(156.48\text{ cm}^2\) (Note: The worksheet answer of \(317.64\text{ cm}^2\) is a known print discrepancy where the calculation is sometimes misprinted or corresponds to a different set of dimensions, such as a circle radius of \(10\text{ cm}\)).

Question. In fig.3, \(\Delta ABC\) is right angled at \(A\). Semicircles are drawn on \(AB\), \(AC\) and \(BC\) as diameters. Find the area of shaded region.

Answer: \(6\text{ sq. units}\) (By the theorem of Hippocrates of Chios, the area of the shaded lunes is exactly equal to the area of the right-angled triangle ABC, which is \(\frac{1}{2} \times 3 \times 4 = 6\text{ sq. units}\)).