** NCERT Solution For Class 10, Maths, Chapter 10, Circles, Exercise 10.1**, involves basic fundamental of circles like knowledge of tangent, Secant, point of contact etc. **Class 10, Maths chapter 10, Ex.10.1** contains total four questions to study.

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Toggle## Class 10, Maths, Chapter 10, Exercise 10.1 Solutions

**Q.1. How many tangents can a circle have?**

**Ans:** A circle can have an infinite number of tangents.

**Q.2. 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:** (i) only one

(ii) secant

(iii) two

(iv) point of contact

**(See Answer below)**

(i) A tangent to a circle intersects it in **only one** point (s).

(ii) A line intersecting a circle in two points is called a **secant.**

(iii) A circle can have **two** parallel tangents at the most.

(iv) The common point of a tangent to a circle and the circle is called **point of contact.**

**Q.3. 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 :**

**(A) 12 cm **

**(B) 13 cm **

**(C) 8.5 cm **

**(D) $\sqrt{119}\,\,cm$**

**Ans: (D)**

**Q.4. 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: **Here ‘a’ is the given line and a circle with centre O is drawn.

Line PT is drawn || to line ‘a’.

PT is the tangent to the circle.

AB is drawn || to line ‘a’ and is the secant.