**Download NCERT Solutions For Class 10 Maths Chapter 10 Exercise 10.1**

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

**Answer –** A circle can have infinite tangents.

**2. Fill in the blanks**

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

**ii.**A line intersecting the circle in two points is called a

**.**

__secant__**iii.**A circle can have

__parallel tangents at most.__

**two****iv.**The common point of a tangent to a circle and the circle is called

__point of contact__.

**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) √119 cm

Let the length of **PQ** be l

∵ Tangent and radius are perpendicular to each other at point of contact

∴ In △OPQ, ∠P=90°

OP^{2 }+ PQ^{2 }= OQ^{2} (By Pythagorean Theorem)

5^{2} + l^{2} = 12^{2}l^{2} = 12^{2} – 5^{2}l^{2} = 144 – 25

l^{2} = 119

l = √119 cm

Therefore, the correct option is (D)

**Download NCERT Solutions For Class 10 Maths Chapter 10 Exercise 10.1**

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