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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.
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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 two numbers whose sum is 27 and product is 182.
- 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:-
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:-
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.
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Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.
- 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 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:-
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:-
Complete the following statements:
(i) Probability of an event E + Probability of the event ‘not E’ = .
(ii) The probability of an event that cannot happen is . Such an event is called .
(iii) The probability of an event that is certain to happen is . Such an event is called .
(iv) The sum of the probabilities of all the elementary events of an experiment is .(v) The probability of an event is greater than or equal to and less than or equal to .
- Q:-
A game of chance consists of spinning an arrow which comes to rest pointing at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8 (see Fig. 15.5 ), and these are equally likely outcomes. What is the probability that it will point at
(i) 8 ?
(ii) an odd number?
(iii) a number greater than 2?
(iv) a number less than 9?
- 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:-
A jar contains 24 marbles, some are green and others are blue. If a marble is drawn at random from the jar, the probability that it is green is 2/3.
Find the number of blue balls in the jar.
- Q:-
Find two consecutive positive integers, sum of whose squares is 365.
- Q:-
Find two numbers whose sum is 27 and product is 182.
- 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:-
Write down the decimal expansions of those rational numbers in Question 1 above which have terminating decimal expansions.
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