Circles - Theorems and Properties - Problems on Circles

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

Understanding "Circles - Theorems and Properties - Problems on Circles" is crucial for students preparing for school and competitive exams. This topic not only forms a significant part of the curriculum but also helps in developing problem-solving skills. Practicing MCQs and objective questions enhances your grasp of the concepts, making it easier to tackle important questions in exams.

What You Will Practise Here

  • Fundamental properties of circles, including radius, diameter, and circumference.
  • Theorems related to angles subtended by chords and arcs.
  • Properties of tangents and secants, including their lengths and relationships.
  • Understanding cyclic quadrilaterals and their properties.
  • Application of Pythagorean theorem in circle-related problems.
  • Diagrams illustrating key concepts for better visualization.
  • Practice questions that cover a variety of difficulty levels.

Exam Relevance

The topic of circles is frequently tested in CBSE, State Boards, and competitive exams like NEET and JEE. Students can expect questions that assess their understanding of theorems and properties through both direct application and problem-solving scenarios. Common question patterns include multiple-choice questions that require quick reasoning and conceptual clarity.

Common Mistakes Students Make

  • Confusing the properties of tangents and secants, leading to incorrect answers.
  • Misapplying theorems related to angles in circles, especially in complex diagrams.
  • Overlooking the significance of cyclic quadrilaterals in problem-solving.
  • Failing to visualize problems, which can lead to errors in calculations.

FAQs

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

Question: How can I improve my speed in solving circle-related MCQs?
Answer: Regular practice of objective questions and understanding the underlying concepts will significantly enhance your speed and accuracy.

Start solving practice MCQs on "Circles - Theorems and Properties - Problems on Circles" today to test your understanding and boost your confidence for the upcoming exams. Your preparation is the key to success!

Q. A tangent to a circle is drawn from a point outside the circle. If the radius of the circle is 3 cm and the distance from the center to the point is 5 cm, what is the length of the tangent?
  • A. 4 cm
  • B. 6 cm
  • C. 5 cm
  • D. 3 cm
Q. If a circle has an area of 36π cm², what is the radius of the circle?
  • A. 6 cm
  • B. 12 cm
  • C. 9 cm
  • D. 18 cm
Q. If a circle has an area of 36π cm², what is the radius?
  • A. 6 cm
  • B. 12 cm
  • C. 18 cm
  • D. 9 cm
Q. In a circle, if the angle subtended by an arc at the center is 80 degrees, what is the angle subtended at any point on the circumference?
  • A. 40 degrees
  • B. 80 degrees
  • C. 20 degrees
  • D. 60 degrees
Q. In a circle, if two chords AB and CD intersect at point E, and AE = 3 cm, EB = 4 cm, what is the length of segment CE if DE = 2 cm?
  • A. 6 cm
  • B. 8 cm
  • C. 5 cm
  • D. 7 cm
Q. Two circles intersect at points A and B. If the radius of the first circle is 4 cm and the second is 6 cm, what is the maximum distance between the centers of the circles?
  • A. 10 cm
  • B. 8 cm
  • C. 12 cm
  • D. 14 cm
Q. Two circles intersect at points A and B. If the radius of the first circle is 4 cm and the second circle is 6 cm, what is the maximum distance between the centers of the circles?
  • A. 10 cm
  • B. 8 cm
  • C. 2 cm
  • D. 12 cm
Q. What is the area of a sector of a circle with a radius of 10 cm and a central angle of 90 degrees?
  • A. 25π cm²
  • B. 50π cm²
  • C. 75π cm²
  • D. 100π cm²
Q. What is the area of a sector of a circle with a radius of 4 cm and a central angle of 60 degrees?
  • A. 8π/3 cm²
  • B. 4π/3 cm²
  • C. 2π cm²
  • D. 16π/3 cm²
Q. What is the area of a sector of a circle with a radius of 5 cm and a central angle of 120 degrees?
  • A. 25π/3 cm²
  • B. 10π cm²
  • C. 15π/2 cm²
  • D. 20π/3 cm²
Q. What is the length of an arc of a circle with a radius of 3 cm that subtends an angle of 90 degrees at the center?
  • A. π cm
  • B. 1.5π cm
  • C. 3π cm
  • D. 6 cm
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