All Courses
Get the App Signup / Login
Sign in Open App
Class 10 Exam  >  Class 10 Tests  >  Mathematics (Maths) Class 10  >  Case Based Questions Test: Circles - Class 10 MCQ

Case Based Questions Test: Circles - Class 10 MCQ


Test Description

15 Questions MCQ Test Mathematics (Maths) Class 10 - Case Based Questions Test: Circles

Case Based Questions Test: Circles for Class 10 2024 is part of Mathematics (Maths) Class 10 preparation. The Case Based Questions Test: Circles questions and answers have been prepared according to the Class 10 exam syllabus.The Case Based Questions Test: Circles MCQs are made for Class 10 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Case Based Questions Test: Circles below.
Solutions of Case Based Questions Test: Circles questions in English are available as part of our Mathematics (Maths) Class 10 for Class 10 & Case Based Questions Test: Circles solutions in Hindi for Mathematics (Maths) Class 10 course. Download more important topics, notes, lectures and mock test series for Class 10 Exam by signing up for free. Attempt Case Based Questions Test: Circles | 15 questions in 30 minutes | Mock test for Class 10 preparation | Free important questions MCQ to study Mathematics (Maths) Class 10 for Class 10 Exam | Download free PDF with solutions
Case Based Questions Test: Circles - Question 1
Save

Read the following text and answer the following question on the basis of the same:

A farmer has a field in the shape of triangle with AB = 13 cm, BC = 14 cm and AE = 7 cm. He wants to leave a space in the form of a circular field for growing wheat and the remaining for growing vegetables.

Q. The measure of BF is:

Detailed Solution for Case Based Questions Test: Circles - Question 1

∴ AB = 13 cm (given)

∴ BF = AB – AF

= (13 – 7) cm

AE = 7 cm (given)

Then, AF = AE (Tangents of the circle)

⇒ AF = 7 cm.

[Proved, AF = 7 cm]

BF = 6 cm

Case Based Questions Test: Circles - Question 2
Save

Read the following text and answer the following question on the basis of the same:

A farmer has a field in the shape of triangle with AB = 13 cm, BC = 14 cm and AE = 7 cm. He wants to leave a space in the form of a circular field for growing wheat and the remaining for growing vegetables.

Q. The measure of CE + CD is:

Detailed Solution for Case Based Questions Test: Circles - Question 2

∴ AB = 13 cm (given)

∴ BF = AB – AF

BC = 14 cm (given)

= (13 – 7) cm

AE = 7 cm (given)

Then, AF = AE (Tangents of the circle)

⇒ AF = 7 cm.

[Proved, AF = 7 cm]

BF = 6 cm

BF = 6 cm (Proved)

∴ BD = BF (Tangents of the circle)

So, BD = 6 cm.

and BD = 6 cm [Proved]

then CD = BC – BD

= (14 – 6) cm = 8 cm

but CD = CE (Tangents of the circle)

∴ CE = 8 cm

So, CD + CE = (8 + 8) cm = 16 cm.

1 Crore+ students have signed up on EduRev. Have you? Download the App
Case Based Questions Test: Circles - Question 3
Save

Read the following text and answer the following question on the basis of the same:

A farmer has a field in the shape of triangle with AB = 13 cm, BC = 14 cm and AE = 7 cm. He wants to leave a space in the form of a circular field for growing wheat and the remaining for growing vegetables.

Q. The measure of AF is:

Detailed Solution for Case Based Questions Test: Circles - Question 3
AE = 7 cm (given)

Then, AF = AE (Tangents of the circle)

⇒ AF = 7 cm.

Case Based Questions Test: Circles - Question 4
Save

Read the following text and answer the following question on the basis of the same:

A farmer has a field in the shape of triangle with AB = 13 cm, BC = 14 cm and AE = 7 cm. He wants to leave a space in the form of a circular field for growing wheat and the remaining for growing vegetables.

Q. The measure of BD is:
Detailed Solution for Case Based Questions Test: Circles - Question 4

∴ AB = 13 cm (given)

BF = AB – AF

= (13 – 7) cm

[Proved in Q. 1., AF = 7 cm]

BF = 6 cm

BF = 6 cm (Proved)

∴ BD = BF (Tangents of the circle)

So, BD = 6 cm.

Case Based Questions Test: Circles - Question 5
Save

Read the following text and answer the following question on the basis of the same:

A farmer has a field in the shape of triangle with AB = 13 cm, BC = 14 cm and AE = 7 cm. He wants to leave a space in the form of a circular field for growing wheat and the remaining for growing vegetables.

Q. The measure of AC is:
Detailed Solution for Case Based Questions Test: Circles - Question 5

∴ AB = 13 cm (given)

BF = AB – AF

= (13 – 7) cm

AE = 7 cm (given)

Then, AF = AE (Tangents of the circle)

⇒ AF = 7 cm.

[Proved AF = 7 cm]

BF = 6 cm

BC = 14 cm (given)

and BD = 6 cm [Proved in Q. 3]

then CD = BC – BD

= (14 – 6) cm = 8 cm

but CD = CE (Tangents of the circle)

∴ CE = 8 cm

So, CD + CE = (8 + 8) cm = 16 cm.

CE = 8 cm

and AE = 7 cm (given)

then, AC = AE + EC

= (7 + 8) cm

= 15 cm.

Case Based Questions Test: Circles - Question 6
Save

Both Assertion and Reason are true but Reason is not correct explanation of Assertion

In the following figure, a circle with centre O is inscribed in a quadrilateral ABCD such that, it touches the sides BC, AB, AD and CD at points P, Q, R and S respectively. If AB = 29 cm, AD = 23 cm, ∠B = 90° and DS = 5 cm.

Q. Find the value of AR:
Detailed Solution for Case Based Questions Test: Circles - Question 6

Here, AD = 23 cm (given)

and

Here, DS = 5 cm

but DR = DS (Length of tangents are equal)

then DR = 5 cm.

DR = 5 cm (Proved)

then AR = AD – DR cm

= (23 – 5) cm = 18 cm.

Case Based Questions Test: Circles - Question 7
Save

Both Assertion and Reason are true but Reason is not correct explanation of Assertion

In the following figure, a circle with centre O is inscribed in a quadrilateral ABCD such that, it touches the sides BC, AB, AD and CD at points P, Q, R and S respectively. If AB = 29 cm, AD = 23 cm, ∠B = 90° and DS = 5 cm.

Q. Find the value of BP:
Detailed Solution for Case Based Questions Test: Circles - Question 7

AB = 29 cm (given) but AQ = AR(Length of tangents are equal) then AQ = 18 cm

Here, AD = 23 cm (given)

and

Here, DS = 5 cm

but DR = DS (Length of tangents are equal)

then DR = 5 cm.

DR = 5 cm (Proved)

then AR = AD – DR cm

= (23 – 5) cm = 18 cm. [Proved]

∴ BQ = AB – AQ

= (29 – 18) cm = 11 cm.

BQ = 11 cm [Proved]

and BP = BQ (Length of tangents are equal)

∴ BP = 11 cm.

Case Based Questions Test: Circles - Question 8
Save

Both Assertion and Reason are true but Reason is not correct explanation of Assertion

In the following figure, a circle with centre O is inscribed in a quadrilateral ABCD such that, it touches the sides BC, AB, AD and CD at points P, Q, R and S respectively. If AB = 29 cm, AD = 23 cm, ∠B = 90° and DS = 5 cm.

Q. Find the value of DR:
Detailed Solution for Case Based Questions Test: Circles - Question 8
Here, DS = 5 cm

but DR = DS

(Length of tangents are equal)

then DR = 5 cm.

Case Based Questions Test: Circles - Question 9
Save

Both Assertion and Reason are true but Reason is not correct explanation of Assertion

In the following figure, a circle with centre O is inscribed in a quadrilateral ABCD such that, it touches the sides BC, AB, AD and CD at points P, Q, R and S respectively. If AB = 29 cm, AD = 23 cm, ∠B = 90° and DS = 5 cm.

Q. Find the value of QB:
Detailed Solution for Case Based Questions Test: Circles - Question 9

AB = 29 cm (given)

but AQ = AR (Length of tangents are equal)

then AQ = 18 cm

Here, AD = 23 cm (given)

and

Here, DS = 5 cm

but DR = DS (Length of tangents are equal)

then DR = 5 cm.

DR = 5 cm (Proved)

then AR = AD – DR cm

= (23 – 5) cm = 18 cm. [Proved]

∴ BQ = AB – AQ

= (29 – 18) cm = 11 cm.

Case Based Questions Test: Circles - Question 10
Save

Both Assertion and Reason are true but Reason is not correct explanation of Assertion

In the following figure, a circle with centre O is inscribed in a quadrilateral ABCD such that, it touches the sides BC, AB, AD and CD at points P, Q, R and S respectively. If AB = 29 cm, AD = 23 cm, ∠B = 90° and DS = 5 cm.

Q. AR is equal to:
Detailed Solution for Case Based Questions Test: Circles - Question 10
AR = AQ (Length of tangents are equal)
Case Based Questions Test: Circles - Question 11
Save

Read the following text and answer the following questions on the basis of same: 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 attached to the rim in such a way that as the wheel turns, they are kept upright, usually by gravity.

After taking a ride in Ferris wheel Aarti came out from the crowd and was observing her friends who were enjoying the ride. She was curios about the different angles and measures that wheel will form. She forms the figure as given below:

Q. Find ∠RQP
Detailed Solution for Case Based Questions Test: Circles - Question 11

∠RSQ =∠RQP = 75°

[Angles in alternate segment]

Case Based Questions Test: Circles - Question 12
Save

Read the following text and answer the following questions on the basis of same: 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 attached to the rim in such a way that as the wheel turns, they are kept upright, usually by gravity.

After taking a ride in Ferris wheel Aarti came out from the crowd and was observing her friends who were enjoying the ride. She was curios about the different angles and measures that wheel will form. She forms the figure as given below:

Q. Find ∠ORP
Detailed Solution for Case Based Questions Test: Circles - Question 12
Radius is always perpendicular to the tangent.
Case Based Questions Test: Circles - Question 13
Save

Read the following text and answer the following questions on the basis of same: 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 attached to the rim in such a way that as the wheel turns, they are kept upright, usually by gravity.

After taking a ride in Ferris wheel Aarti came out from the crowd and was observing her friends who were enjoying the ride. She was curios about the different angles and measures that wheel will form. She forms the figure as given below:

Q. In the given figure, Find ∠ROQ
Detailed Solution for Case Based Questions Test: Circles - Question 13
∠ROQ +∠RPQ = 180°

∠ROQ + 30° = 180°

∠ROQ = 150°

Case Based Questions Test: Circles - Question 14
Save

Read the following text and answer the following questions on the basis of same: 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 attached to the rim in such a way that as the wheel turns, they are kept upright, usually by gravity.

After taking a ride in Ferris wheel Aarti came out from the crowd and was observing her friends who were enjoying the ride. She was curios about the different angles and measures that wheel will form. She forms the figure as given below:

Q. Find ∠RSQ
Detailed Solution for Case Based Questions Test: Circles - Question 14

Case Based Questions Test: Circles - Question 15
Save

Read the following text and answer the following questions on the basis of same: 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 attached to the rim in such a way that as the wheel turns, they are kept upright, usually by gravity.

After taking a ride in Ferris wheel Aarti came out from the crowd and was observing her friends who were enjoying the ride. She was curios about the different angles and measures that wheel will form. She forms the figure as given below:

Q. Find ∠ORQ
Detailed Solution for Case Based Questions Test: Circles - Question 15
In triangle ORQ,

∠ORQ + ∠OQR + ∠ROQ= 180°

2∠ORQ = 180° – ∠ROQ

2∠ORQ = 180° – 150° = 30°

∠ORQ = 15°

123 videos|457 docs|77 tests
Join Course
Information about Case Based Questions Test: Circles Page
In this test you can find the Exam questions for Case Based Questions Test: Circles solved & explained in the simplest way possible. Besides giving Questions and answers for Case Based Questions Test: Circles, EduRev gives you an ample number of Online tests for practice

Top Courses for Class 10

123 videos|457 docs|77 tests
Join Course
Download as PDF

Top Courses for Class 10

Important Questions for Case Based Questions Test: Circles

Find all the important questions for Case Based Questions Test: Circles at EduRev.Get fully prepared for Case Based Questions Test: Circles with EduRev's comprehensive question bank and test resources. Our platform offers a diverse range of question papers covering various topics within the Case Based Questions Test: Circles syllabus. Whether you need to review specific subjects or assess your overall readiness, EduRev has you covered. The questions are designed to challenge you and help you gain confidence in tackling the actual exam. Maximize your chances of success by utilizing EduRev's extensive collection of Case Based Questions Test: Circles resources.

Case Based Questions Test: Circles MCQs with Answers

Prepare for the Case Based Questions Test: Circles within the Class 10 exam with comprehensive MCQs and answers at EduRev. Our platform offers a wide range of practice papers, question papers, and mock tests to familiarize you with the exam pattern and syllabus. Access the best books, study materials, and notes curated by toppers to enhance your preparation. Stay updated with the exam date and receive expert preparation tips and paper analysis. Visit EduRev's official website today and access a wealth of videos and coaching resources to excel in your exam.

Online Tests for Case Based Questions Test: Circles Mathematics (Maths) Class 10

Practice with a wide array of question papers that follow the exam pattern and syllabus. Our platform offers a user-friendly interface, allowing you to track your progress and identify areas for improvement. Access detailed solutions and explanations for each test to enhance your understanding of concepts. With EduRev's Online Tests, you can build confidence, boost your performance, and ace Case Based Questions Test: Circles with ease. Join thousands of successful students who have benefited from our trusted online resources.
© EduRev
Education Revolution
Follow Us
Signup to see your scores go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup