-
Q1 How many tangents can a circle have?
Ans: Circle is the locus of points equidistant from a given point, which is the centre of the circle. And, tangent is the line which intersects a circle at one point only. On these points which touches at only one point. Hence, a circle can have infinite tangents.
Q2 Fill in the blanks :
(i) A tangent to a circle intersects it in point (s).
(ii) A line intersecting a circle in two points is called a .
(iii) A circle can have parallel tangents at the most.
(iv) The common point of a tangent to a circle and the circle is called .Ans: - A tangent to a circle intersect it in one point.
- A line intersecting a circle in two points is called a secant.
- A circle can have two parallel tangent s at the most.
- The common point of a tangent of a circle and the circle is called point of contact.
Q3 A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q so that OQ = 12 cm. Length PQ is:
Ans: 
Q4 Draw a circle and two lines parallel to a given line such that one is a tangent and the other, a secant to the circle.
Ans: In the given figure , AB and BC are two parallel lines. The line segment BC is the tangent at point x while AB is the secant to the circle.
Circles Question Answers: NCERT Class 10 Mathematics
Welcome to the Chapter 10 - Circles, Class 10 Mathematics - NCERT Solutions page. Here, we provide detailed question answers for Chapter 10 - Circles.The page is designed to help students gain a thorough understanding of the concepts related to natural resources, their classification, and sustainable development.
Our solutions explain each answer in a simple and comprehensive way, making it easier for students to grasp key topics Tangent to a circle, properties of tangents, perpendicularity of tangents to radii and excel in their exams. By going through these Circles question answers, you can strengthen your foundation and improve your performance in Class 10 Mathematics. Whether you're revising or preparing for tests, this chapter-wise guide will serve as an invaluable resource.
Download PDF - Chapter 10 Circles - Class 10 Mathematics
Download PDF - NCERT Examplar Solutions - Chapter 10 Circles - Class 10 Mathematics
Exercise 1 ( Page No. : 209 )
Exercise 2 ( Page No. : 214 )
Key Features of NCERT Class 10 Mathematics Chapter 'Circles' question answers :
- All chapter question answers with detailed explanations.
- Simple language for easy comprehension.
- Aligned with the latest NCERT guidelines.
- Perfect for exam preparation and revision.
Popular Questions of Class 10 Mathematics
- Q:-
Is the following situation possible? If so, determine their present ages.
The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48. - Q:-
A cottage industry produces a certain number of pottery articles in a day. It was observed on a particular day that the cost of production of each article (in rupees) was 3 more than twice the number of articles produced on that day. If the total cost of production on that day was Rs 90, find the number of articles produced and the cost of each article.
- Q:-
Find two consecutive positive integers, sum of whose squares is 365.
- Q:-
Find the nature of the roots of the following quadratic equations. If the real roots exist, find them:
(i) 2x2 – 3x + 5 = 0
(iii) 2x2– 6x + 3 = 0 - Q:-
Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.
(i) x2 – 2x – 8 (ii) 4s2 – 4s + 1 (iii) 6x2 – 3 – 7x (iv) 4u2 + 8u (v) t2 – 15 (vi) 3x2 – x – 4
- Q:-
Find two numbers whose sum is 27 and product is 182.
- Q:-
Refer to Example 13. (i) Complete the following table:
(ii) A student argues that ‘there are 11 possible outcomes 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12. Therefore, each of them has a probability
Do you agree with this argument? Justify your answer.
- Q:-
Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.
- Q:-
Two poles of equal heights are standing opposite each other on either side of the road, which is 80 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 60° and 30°, respectively. Find the height of the poles and the distances of the point from the poles.
- Q:-
The graphs of y = p(x) are given in Fig. 2.10 below, for some polynomials p(x). Find the number of zeroes of p(x), in each case.
Recently Viewed Questions of Class 10 Mathematics
- Q:-
A statue, 1.6 m tall, stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60° and from the same point the angle of elevation of the top of the pedestal is 45°. Find the height of the pedestal.
- Q:-
Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre.
- Q:-
Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.
- Q:-
The angle of elevation of the top of a building from the foot of the tower is 30° and the angle of elevation of the top of the tower from the foot of the building is 60°. If the tower is 50 m high, find the height of the building.
- Q:-
A game consists of tossing a one rupee coin 3 times and noting its outcome each time. Hanif wins if all the tosses give the same result i.e., three heads or three tails, and loses otherwise. Calculate the probability that Hanif will lose the game.
- Q:-
Two poles of equal heights are standing opposite each other on either side of the road, which is 80 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 60° and 30°, respectively. Find the height of the poles and the distances of the point from the poles.
- Q:-
The angles of elevation of the top of a tower from two points at a distance of 4 m and 9 m from the base of the tower and in the same straight line with it are complementary. Prove that the height of the tower is 6 m.
- Q:-
The cost of 2 kg of apples and 1kg of grapes on a day was found to be ` 160. After a month, the cost of 4 kg of apples and 2 kg of grapes is ` 300. Represent the situation algebraically and geometrically.
- Q:-
Give examples of polynomials p(x), g(x), q(x) and r(x), which satisfy the division algorithm and
(i) deg p(x) = deg q(x) (ii) deg q(x) = deg r(x) (iii) deg r(x) = 0
- Q:-
(i) A lot of 20 bulbs contain 4 defective ones. One bulb is drawn at random from the lot. What is the probability that this bulb is defective?
(ii) Suppose the bulb drawn in (i) is not defective and is not replaced. Now one bulb is drawn at random from the rest. What is the probability that this bulb is not defective ?
- All Chapters Of Class 10 Mathematics
- All Subjects Of Class 10