Class 10 Math Circles MCQ Test

Class 10 Math Circles MCQ Test: Boost your knowledge with free online multiple-choice questions for CBSE Class 10 Math Chapter 10. Master the properties of circles, including tangents, chords, and arcs. Ideal for CBSE exam preparation and competitive tests.

Class 10 Math Circles MCQ Test Quiz

Time: 10 Minutes for 10 Question.

10th Math: Circles

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About Circles MCQ Test

Chapter 10 of the CBSE Class 10 Math curriculum, titled “Circles,” covers essential properties and theorems related to circles. This chapter includes the study of tangents, chords, and arcs, as well as their various properties and applications. The free MCQ quiz provided in this chapter will help students solidify their understanding and prepare effectively for their CBSE examinations.

Key Concepts Covered:

Basic Properties of Circles:
- Definition: A circle is a set of all points in a plane that are at a fixed distance (radius) from a given point (center).
- Radius: The distance from the center of the circle to any point on the circle.
- Diameter: The distance across the circle through the center, equal to twice the radius.
Chords and Their Properties:
- Chord: A line segment with both endpoints on the circle.
- Perpendicular from the Center: A perpendicular from the center of the circle to a chord bisects the chord and vice versa.
- Equal Chords: Chords that are equidistant from the center are equal in length.
Tangents to a Circle:
- Definition: A tangent is a line that touches the circle at exactly one point.
- Properties:
  - The tangent at any point of a circle is perpendicular to the radius at that point.
  - Two tangents drawn from an external point to a circle are equal in length.
Theorems Related to Circles:
- Angle Subtended by a Chord: Angles subtended by the same chord at the circumference of the circle are equal.
- Angle in a Semicircle: The angle subtended by a diameter of the circle is a right angle.
- Angles in the Same Segment: Angles subtended by the same chord or arc in the same segment are equal.
Properties of Tangents and Secants:
- Secant: A line that intersects the circle at two points.
- Power of a Point: The power of a point with respect to a circle is defined as the square of the length of the tangent from that point to the circle. It is also equal to the product of the lengths of the segments of any secant drawn from that point.
Length of Tangent from a Point:
- Formula: If a tangent is drawn from a point
  
  $P$ to a circle with center
  
  $O$ and radius
  
  $r$ , and the distance from
  
  $P$ to
  
  $O$ is
  
  $d$ , then the length of the tangent
  
  $l$ is given by: $\sqrt{d^2 – r^2}$
  
  $l = d^{2} - r^{2}$
Applications of Circle Properties:
- Real-Life Problems: Use the properties of circles to solve problems in geometry, design, and various practical scenarios.
- Example: Calculating the length of a tangent from a point outside the circle or finding the radius when given the length of a chord and the distance from the center.

Quiz Structure:

The MCQ quiz for this chapter includes a series of questions designed to test students’ understanding of the properties and theorems related to circles. Questions cover topics such as chords, tangents, angles, and their respective properties. The interactive format allows students to practice and assess their knowledge effectively.

Conclusion:

Practicing with the Class 10 Math Circles MCQ Test Chapter 10 is an excellent way for CBSE students to reinforce their understanding of circle properties and theorems. This chapter provides a comprehensive exploration of circles, including their basic properties, chords, tangents, and practical applications. The MCQ quiz helps ensure students are well-prepared for their academic assessments and competitive exams.

Sanjay Kumar

Math educator (6-12) with an MSc from Delhi University and quiz content creator at QuizRanker.org.