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CBSE Class 10  >  Class 10 Test  >  Olympiad Preparation  >  Math Olympiad Test: Circles- 2 - Class 10 MCQ

Math Olympiad Test: Circles- 2 - Free MCQ with solutions Class 10


MCQ Practice Test & Solutions: Math Olympiad Test: Circles- 2 (15 Questions)

You can prepare effectively for Class 10 Olympiad Preparation for Class 10 with this dedicated MCQ Practice Test (available with solutions) on the important topic of "Math Olympiad Test: Circles- 2". These 15 questions have been designed by the experts with the latest curriculum of Class 10 2026, to help you master the concept.

Test Highlights:

  • - Format: Multiple Choice Questions (MCQ)
  • - Duration: 15 minutes
  • - Number of Questions: 15

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Math Olympiad Test: Circles- 2 - Question 1
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The perimeter of a sector of a circle of radius 5.2 cm is 16.4 cm, then what is area of sector?

Detailed Solution: Question 1

Let O be the centre of a circle of radius 5.2 cm. Let OABO be the sector with perimeter 16.4 cm.

OA + O B + arc AB = 27.2
5.2 + 5 .2 + arc AB = 16.4
⇒ arc AB = 16.4 - 16.4 = 6 cm
Area of sector OACBO

Math Olympiad Test: Circles- 2 - Question 2
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A bicycle wheel makes 5000 revolutions in moving 11 km. What is the radius  of the wheel?

Detailed Solution: Question 2

Distance moved by wheel 
= 2 × π × r × 5000 = 11000 m

= 35 cm

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Math Olympiad Test: Circles- 2 - Question 3
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What is the length of tangent drawn from a point whose distance from the centre of a circle is 25 cm, if radius of the circle is 7 cm?

Detailed Solution: Question 3

PT2 + OT2 = OP2
⇒ PT2 = (25)2 -(7)2
⇒ PT = = 24 cm.

Math Olympiad Test: Circles- 2 - Question 4
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A bucket is raised from a well by means of a rope which is wound round a wheel of diameter 77 cm. Given that the bucket ascends in 1 minute 28 seconds with a uniform speed of 1.1 m/s. What is the number of complete revolutions the wheel makes in raising the bucket?

Detailed Solution: Question 4

Distance moved by rope
= (1.1) × (60 + 28)
∴ No. of revolutions = 

Math Olympiad Test: Circles- 2 - Question 5
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What is the value of y and x respectively in the given figure?

Detailed Solution: Question 5

In ΔABO,
∠y + 25° + 100° = 180°
⇒ y = 55°
∠C + ∠A = 180° [∵ ABCD is cycle]
⇒ ∠ = 80°
In ΔPBC,
∠x + 55° + 80° = 180°
⇒ ∠x = 45°

Math Olympiad Test: Circles- 2 - Question 6
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AB is a tangent to the circle at E. If EC = ED and ∠CDE = 62°. Find angle ∠AED.

Detailed Solution: Question 6

∵ EC = ED
∴ ∠ECD = ∠EDC = 62°
∴ ∠DEC = 180° - (2 × 62°) =56°

∴ ∠AED = ∠CED + ∠AEC
= 56° + 62° = 118°

Math Olympiad Test: Circles- 2 - Question 7
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In the given figure AD is diameter of the circle. If ∠BCD = 130°. What is the value of ∠DAB?

Detailed Solution: Question 7

∵ A, B, C and D are on the circumference of the circle
∴ ABCD is a cyclic quadrilateral, i.e.,
∠A + ∠C = 180°
⇒ ∠A = 180° - ∠C = 180° - 130° = 50°
∴ ∠DAB= 50°.

Math Olympiad Test: Circles- 2 - Question 8
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What is the area of quadrant of a circle whose circumference is 22 cm?

Detailed Solution: Question 8

Let r be the radius
2πr = 22

Area of quadrant = 

Math Olympiad Test: Circles- 2 - Question 9
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In a circle of radius 10.5 cm, the minor arc is one-fifth of the major arc. What is the area of major arc?

Detailed Solution: Question 9

Let the major arc be x cm
Length of minor arc = x/5
Circumference = 
⇒ 
⇒ 
⇒ x = 55 cm
Required area = 
=    288.75 cm2.

Math Olympiad Test: Circles- 2 - Question 10
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A Pendulum swings through an angle of 30° and describes an arc 8.8 cm in length, then what is the length of the Pendulum?

Detailed Solution: Question 10

Length of pendulum
= radius of the sector = x cm
Arc length = 8.8 cm
⇒ 

Math Olympiad Test: Circles- 2 - Question 11
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The minute hand of a clock is 12 cm long. Find the area of the face of the clock described by the minute hand in 35 minutes.

Detailed Solution: Question 11

Angle described by the minute hand in 35 minutes = 
θ = 210º, r = 12 cm
Area of the sector = 

= 264 cm2.

Math Olympiad Test: Circles- 2 - Question 12
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In the given figure, ΔABC is right angled at A with AB = 6 cm and AC = 8 cm. A circle with centre O has been inscribed inside the triangle. Find the value of the radius of the inscribed circle.

Detailed Solution: Question 12



(area ΔOAC) + (area ΔOAB) + (area ΔOBC)
= area (ΔABC)



⇒ 8r + 6r + 10r = 48
⇒ 24r = 48 ⇒ r = 2

Math Olympiad Test: Circles- 2 - Question 13
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A chord of a circle of radius 14 cm makes a right angle at the centre. Find the area of minor segment of the circle.

Detailed Solution: Question 13

Area of the sector OACBO,

= 154 cm2.
Area of ΔOAB = 

∴ Area of minor segment of circle
= 154 - 98 = 56 cm2.

Math Olympiad Test: Circles- 2 - Question 14
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A field is in the form of a circle. The cost of ploughing the field at Rs. 1.50 per m2 is Rs. 5775. Find the cost of fencing the field at Rs. 8.50 per meter.

Detailed Solution: Question 14

Area of the circular filed = 
πr2 = 3850

r = 35 m
Circumference = 2πr = = 220 m
Cost of fencing = 220 × 8.50 = Rs. 1870

Math Olympiad Test: Circles- 2 - Question 15
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What is the area of shaded region if ABCD is a square of side 14 cm and APD and BPC are semi circles?

Detailed Solution: Question 15

Area of the shaded region = Area of square ABCD - Area of two semicircles

= 196 - 154 = 42 cm2

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About this Class 10 Practice Test

This test contains 15 MCQs on Math Olympiad Test: Circles- 2 with detailed solutions for each question. It is part of the Olympiad Preparation for Class 10 course on EduRev, designed to align with the current Class 10 syllabus. Each solution explains not just the correct answer but also gives you an understanding of the topic — not just to attempt the question but also help you prepare for the exam with practice.

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