NCERT Solutions For Class 10 Maths Chapter 10 Circles Exercise 10.1 - 2025-26

Exercise 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.

Conclusion

Vedantu's NCERT Maths Chapter 10 Class 10 Circles Exercise 10.1 Solutions includes detailed solutions and explanations to all questions. We will understand the properties of circles and tangents, especially the relationship between the radius and the tangent at the point of contact. By practising these exercises, we strengthen these concepts and learn the theorems about tangents. Ex 10.1 Class 10 solutions will help you develop an excellent foundation in circle geometry and prepare you for exams.

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Chapter-Specific NCERT Solutions for Class 10 Maths

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