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NCERT Solutions for Class 10 Maths Chapter 10 Circles
NCERT Solutions for Class 10 Maths Chapter 10: Circles - Exercise 10.1
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EXERCISE NO: 10.1
1.How many tangents can a circle have?
Ans: A circle can have an infinite number of tangents. A circle is made of infinite points and from each point, a tangent can be formed.
2. Fill in the blanks :
(i) A tangent to a circle intersects it in _________ point(s).
Ans: A tangent to a circle intersects it in exactly one point.
(ii) A line intersecting a circle in two points is called a _______.
Ans: A line intersecting a circle in two points is called a secant.
(iii) A circle can have _______ parallel tangents at the most.
Ans: A circle can have two parallel tangents at the most opposite to one another.
(iv) The common point of a tangent to a circle and the circle is called ______.
Ans: The common point of a tangent to a circle and the circle is called the Point of Contact.
3. A tangent PQ at a point P of a circle of radius \[\text{5cm}\] meets a line through the centre O at a point Q so that \[\text{OQ = 12cm}\]. Length of PQ is :
(A) \[\text{12}\]cm
(B) \[\text{13}\]cm
(C) \[\text{8}\text{.5}\] cm
(D)\[\sqrt{\text{119}}\]
Ans: According to the Pythagoras Theorem: \[PQ=\sqrt{\left( O{{Q}^{2}}-\left. O{{P}^{2}} \right) \right.}\]
OQ = \[\text{12}\]cm, OP = \[\text{5}\]cm
Because,
\[PQ=\sqrt{\left( O{{Q}^{2}}-\left. O{{P}^{2}} \right) \right.}\]
\[=\sqrt{\left( {{12}^{2}}-\left. {{5}^{2}} \right) \right.}\]
\[=\sqrt{144-25}\]
\[=\sqrt{119}\]cm.
Hence, (D) is the answer.
4. Draw a circle and two lines parallel to a given line such that one is tangent and the other, a secant to the circle.
Ans: From the Given Figure below,
Let ‘l’ be the given line and a circle with centre O is drawn.
A tangent to the circle from point B is drawn \[\parallel \] to line ‘l’.
CD is drawn \[\parallel \] to line ‘l’ and is the secant.
NCERT Solutions for Class 10 Maths Chapter 10 Circles Exercise 10.1
Opting for the NCERT solutions for Ex 10.1 Class 10 Maths is considered as the best option for the CBSE students when it comes to exam preparation. This chapter consists of many exercises. Out of which we have provided the Exercise 10.1 Class 10 Maths NCERT solutions on this page in PDF format. You can download this solution as per your convenience or you can study it directly from our website/ app online.
Vedantu in-house subject matter experts have solved the problems/ questions from the exercise with the utmost care and by following all the guidelines by CBSE. Class 10 students who are thorough with all the concepts from the Subject Maths textbook and quite well-versed with all the problems from the exercises given in it, then any student can easily score the highest possible marks in the final exam. With the help of this Class 10 Maths Chapter 10 Exercise 10.1 solutions, students can easily understand the pattern of questions that can be asked in the exam from this chapter and also learn the marks weightage of the chapter. So that they can prepare themselves accordingly for the final exam.
Besides these NCERT solutions for Class 10 Maths Chapter 10 Exercise 10.1, there are plenty of exercises in this chapter which contain innumerable questions as well. All these questions are solved/answered by our in-house subject experts as mentioned earlier. Hence all of these are bound to be of superior quality and anyone can refer to these during the time of exam preparation. In order to score the best possible marks in the class, it is really important to understand all the concepts of the textbooks and solve the problems from the exercises given next to it.
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