CBSE-Class-10-Maths-Assertion-and-Reason-Chapter-10-Circles

Class 10^th Maths Chapter Assertion and Reason Questions

Question 1

Assertion (A): The tangent to a circle is perpendicular to the radius at the point of contact.
Reason (R): The angle between a tangent and the radius drawn to the point of contact is always $90^\circ$ .

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: A) Both A and R are true, and R is the correct explanation of A.
Explanation: By definition, a tangent is always perpendicular to the radius at the point where it touches the circle.

Question 2

Assertion (A): A circle can have more than two parallel tangents.
Reason (R): Tangents to a circle are equidistant from the center.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: D) A is false, but R is true.
Explanation: A circle can only have two parallel tangents at most, on opposite sides. However, tangents are equidistant from the center.

Question 3

Assertion (A): The radius of a circle is perpendicular to the tangent at the point of contact.
Reason (R): The perpendicular drawn from the center of the circle to a chord bisects the chord.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: B) Both A and R are true, but R is not the correct explanation of A.
Explanation: The radius being perpendicular to the tangent is a separate property from the perpendicular bisector of a chord.

Question 4

Assertion (A): Two tangents can be drawn to a circle from an external point.
Reason (R): The length of tangents drawn from an external point to a circle are equal.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: B) Both A and R are true, but R is not the correct explanation of A.
Explanation: While both statements are true, they are separate properties of tangents to a circle.

Question 5

Assertion (A): If two circles touch each other externally, then the distance between their centers is equal to the sum of their radii.
Reason (R): The sum of radii is only applicable when the circles touch internally.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: C) A is true, but R is false.
Explanation: For external touching circles, the distance between centers is indeed the sum of the radii, not for internal touching circles.

Question 6

Assertion (A): If two circles touch each other internally, then the distance between their centers is equal to the difference of their radii.
Reason (R): For internally touching circles, the common point is on both circles' circumferences.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: A) Both A and R are true, and R is the correct explanation of A.
Explanation: When circles touch internally, the distance between the centers is equal to the difference of their radii.

Question 7

Assertion (A): A tangent to a circle can pass through the center.
Reason (R): Tangents always lie outside the circle except at the point of contact.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: D) A is false, but R is true.
Explanation: A tangent cannot pass through the center; otherwise, it would intersect the circle, violating the definition of a tangent.

Question 8

Assertion (A): Tangents drawn from an external point to a circle subtend equal angles at the center.
Reason (R): The lengths of tangents drawn from an external point to a circle are equal.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: B) Both A and R are true, but R is not the correct explanation of A.
Explanation: Both statements are true, but equal angles at the center are due to symmetry and not solely because of equal tangent lengths.

Question 9

Assertion (A): In a circle, the length of a chord increases as the distance from the center decreases.
Reason (R): The longest chord of a circle is its diameter.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: B) Both A and R are true, but R is not the correct explanation of A.
Explanation: While both statements are correct, the reason does not explain the relationship between chord length and distance from the center.

Question 10

Assertion (A): In a circle, the perpendicular drawn from the center of the circle to a chord bisects the chord.
Reason (R): Any line from the center perpendicular to a chord divides the chord into two equal parts.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: A) Both A and R are true, and R is the correct explanation of A.
Explanation: This is a known property of circles, so the reason is a direct explanation for the assertion.

Question 11

Assertion (A): If two tangents are drawn from an external point to a circle, the angle between them at the external point is bisected by the line segment joining the center and the external point.
Reason (R): The line segment joining the center of the circle to the external point is perpendicular to both tangents.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: C) A is true, but R is false.
Explanation: The line joining the center and the external point does bisect the angle, but it is not perpendicular to both tangents.

Question 12

Assertion (A): In a circle, the distance of a chord from the center is always less than the radius.
Reason (R): The radius is the longest line segment from the center to the circumference of the circle.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: B) Both A and R are true, but R is not the correct explanation of A.
Explanation: While both statements are true, the distance of a chord from the center being less than the radius does not depend on the radius being the longest segment.

Question 13

Assertion (A): If two circles intersect, the line joining their centers passes through the points of intersection.
Reason (R): The line joining the centers of two intersecting circles is the perpendicular bisector of the common chord.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: A) Both A and R are true, and R is the correct explanation of A.
Explanation: The line joining the centers bisects the common chord perpendicularly and passes through the intersection points.

Question 14

Assertion (A): In a circle, a tangent at any point of the circle is perpendicular to the diameter passing through the point.
Reason (R): A tangent is perpendicular to the radius at the point of contact.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: A) Both A and R are true, and R is the correct explanation of A.
Explanation: The tangent is indeed perpendicular to the radius, which includes any diameter passing through that point.

Question 15

Assertion (A): The lengths of tangents drawn from an external point to a circle are equal.
Reason (R): Tangents from an external point to a circle are always parallel.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: C) A is true, but R is false.
Explanation: Tangents from the same external point are equal in length but not necessarily parallel.

Question 16

Assertion (A): A circle can have an infinite number of tangents.
Reason (R): A tangent only touches the circle at one point and does not intersect it.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: B) Both A and R are true, but R is not the correct explanation of A.
Explanation: While both statements are correct, the infinite nature of tangents is unrelated to how they interact with the circle at one point.

Question 17

Assertion (A): The line joining the center of a circle to the midpoint of a chord is perpendicular to the chord.
Reason (R): Every chord has a unique radius that passes through its midpoint.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: C) A is true, but R is false.
Explanation: The radius perpendicular to a chord passes through its midpoint, but not every radius passes through a chord’s midpoint.

Question 18

Assertion (A): Two circles with the same radius can intersect at two points.
Reason (R): Two circles can touch each other at two points if they are of equal radius.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: C) A is true, but R is false.
Explanation: Two circles can intersect at two points, but circles touching at two points is not possible.

Question 19

Assertion (A): The radius of a circle is always less than any tangent drawn to it.
Reason (R): A tangent intersects the circle at two points.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: D) A is false, but R is true.
Explanation: A tangent only touches a circle at one point.

Question 20

Assertion (A): The angle between a radius and a tangent is $90^\circ$ .
Reason (R): A tangent to a circle is always perpendicular to a radius at the point of contact.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: A) Both A and R are true, and R is the correct explanation of A.
Explanation: This is a fundamental property of tangents and circles.

Question 21

Assertion (A): The shortest distance from a point outside a circle to the circle is along the line segment joining the point to the nearest point on the circle.
Reason (R): A perpendicular distance is always the shortest distance.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: A) Both A and R are true, and R is the correct explanation of A.
Explanation: The shortest distance to a point on a circle from an external point is along the perpendicular from the point.

Question 22

Assertion (A): If a line touches a circle, it must be perpendicular to the radius.
Reason (R): Any line touching a circle intersects the circle at only one point.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: B) Both A and R are true, but R is not the correct explanation of A.
Explanation: A tangent is perpendicular to the radius, but intersecting at one point is independent of this property.

Question 23

Assertion (A): The longest chord in a circle is the diameter.
Reason (R): A diameter divides the circle into two equal halves.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: B) Both A and R are true, but R is not the correct explanation of A.
Explanation: While both are true, a chord’s length is not directly related to it dividing the circle into equal halves.

Question 24

Assertion (A): A line perpendicular to a radius at its endpoint on the circle is tangent to the circle.
Reason (R): A tangent is perpendicular to the radius at the point of contact.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: A) Both A and R are true, and R is the correct explanation of A.
Explanation: This is a key characteristic of a tangent’s relationship with a circle.

Question 25

Assertion (A): A circle has infinite tangents.
Reason (R): A tangent intersects a circle at two points.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: C) A is true, but R is false.
Explanation: A tangent touches a circle at only one point, not two.

Chapter 10 Circles

Class 10th Maths Chapter Assertion and Reason Questions