# Circles : Exercise 10.1 (Mathematics NCERT Class 10th)

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

* Sol.* 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 ______.**

**Sol.****(i)**exactly one

**(ii)**secant

**(iii)**two

**(iv)**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 of PQ is : **

** (A) 12 cm (B) 13 cm (C) 8.5 cm (D) **

* Sol.* (D). Because,

**Q.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.
**

*The required figure is as under :*

**Sol.**Here is the given line and a circle with centre O is drawn.

Line PT is drawn || to line .

PT is the tangent to the circle.

AB is drawn || to line and is the secant.

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