Circles - Theorems and Properties - Problems on Circles - Case Studies

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Circles - Theorems and Properties - Problems on Circles - Case Studies MCQ & Objective Questions

Understanding "Circles - Theorems and Properties - Problems on Circles - Case Studies" is crucial for students aiming to excel in their exams. This topic not only forms a significant part of the syllabus but also helps in developing a strong foundation in geometry. Practicing MCQs and objective questions enhances your problem-solving skills and boosts your confidence, making it easier to tackle important questions in exams.

What You Will Practise Here

  • Key theorems related to circles, including theorems on tangents and chords.
  • Properties of circles, such as angles subtended by arcs and cyclic quadrilaterals.
  • Formulas for calculating the area and circumference of circles.
  • Real-life applications of circles in case studies and problem-solving scenarios.
  • Diagrams illustrating various properties and theorems of circles.
  • Common problem types and strategies for solving circle-related questions.
  • Conceptual definitions and terminologies associated with circles.

Exam Relevance

The topic of circles is frequently tested in CBSE, State Boards, NEET, and JEE exams. Students can expect questions that require them to apply theorems and properties in various contexts. Common question patterns include multiple-choice questions that assess both theoretical knowledge and practical application, making it essential to be well-prepared with important Circles - Theorems and Properties - Problems on Circles - Case Studies questions for exams.

Common Mistakes Students Make

  • Misunderstanding the relationship between angles and arcs, leading to incorrect answers.
  • Overlooking the conditions required for certain theorems to apply.
  • Failing to accurately interpret diagrams, which can result in errors in calculations.
  • Confusing properties of tangents and secants, especially in complex problems.

FAQs

Question: What are the key theorems related to circles that I should focus on?
Answer: Important theorems include the tangent-secant theorem, the angle subtended by a chord, and properties of cyclic quadrilaterals.

Question: How can I improve my problem-solving skills for circle-related questions?
Answer: Regular practice of MCQs and understanding the application of theorems will significantly enhance your skills.

Now is the time to take charge of your exam preparation! Dive into solving practice MCQs on "Circles - Theorems and Properties - Problems on Circles - Case Studies" and test your understanding. Every question you tackle brings you one step closer to success!

Q. If the diameter of a circle is 12 cm, what is the area of the circle?
  • A. 36π cm²
  • B. 144π cm²
  • C. 72π cm²
  • D. 24π cm²
Q. If two chords AB and CD intersect at point E inside a circle, and AE = 3 cm, EB = 4 cm, what is the length of CE if ED = 6 cm?
  • A. 2 cm
  • B. 3 cm
  • C. 4 cm
  • D. 5 cm
Q. If two chords AB and CD intersect at point E inside a circle, and AE = 3 cm, EB = 4 cm, what is the length of CE if DE = 2 cm?
  • A. 6 cm
  • B. 8 cm
  • C. 4 cm
  • D. 5 cm
Q. In a circle, if the angle subtended by a chord at the center is 120 degrees, what is the angle subtended by the same chord at any point on the circle?
  • A. 30 degrees
  • B. 60 degrees
  • C. 90 degrees
  • D. 120 degrees
Q. In a circle, if the angle subtended by an arc at the center is 120 degrees, what is the angle subtended at any point on the remaining part of the circle?
  • A. 60 degrees
  • B. 120 degrees
  • C. 90 degrees
  • D. 30 degrees
Q. In a circle, if the diameter is 12 cm, what is the length of the radius?
  • A. 6 cm
  • B. 12 cm
  • C. 3 cm
  • D. 24 cm
Q. In a circle, if the radius is 7 cm, what is the area of the circle?
  • A. 154 cm²
  • B. 49 cm²
  • C. 28 cm²
  • D. 100 cm²
Q. What is the distance between the center of a circle and a point on the circle?
  • A. Diameter
  • B. Circumference
  • C. Radius
  • D. Chord
Q. What is the length of an arc of a circle with a radius of 10 cm and a central angle of 90 degrees?
  • A. 15.7 cm
  • B. 25 cm
  • C. 17.5 cm
  • D. 20 cm
Q. What is the length of the radius of a circle if the area is 50π cm²?
  • A. 5 cm
  • B. 10 cm
  • C. 7 cm
  • D. 8 cm
Q. What is the relationship between the angles formed by two tangents drawn from a point outside the circle?
  • A. They are equal
  • B. They are supplementary
  • C. They are complementary
  • D. They are congruent
Q. What is the relationship between the angles subtended by the same arc at the center and at the circumference of the circle?
  • A. The angle at the center is half of the angle at the circumference
  • B. The angle at the center is equal to the angle at the circumference
  • C. The angle at the center is double the angle at the circumference
  • D. There is no relationship
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