Bihar Board Class 10th Maths Solutions Chapter 10 Circles Ex 10.1 Textbook Questions and Answers.

## BSEB Bihar Board Class 10th Maths Solutions Chapter Chapter 10 Circles Ex 10.1

Question 1.

How many tangents can a circle have?

Solution:

A circle can have an infinite number of tangents.

Question 2.

Fill in the blanks :

- A tangent to a circle intersects it in ________ point(s).
- A line intersecting a circle in two points is called a ________.
- A circle can have ________ parallel tangents at the most.
- The common point of a tangent to a circle and the circle is called ________.

Solution:

- exactly one
- secant
- two
- point of contact

Question 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) \(\sqrt{119}\) cm

Solution:

(D) Because,

PQ = \(\sqrt{\mathrm{OQ}^{2}-\mathrm{OP}^{2}}\)

= \(\sqrt{12^{2}-5^{2}}\) cm

= \(\sqrt{144-25}\) – 25 cm

= \(\sqrt{119}\) cm.

Question 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.

Solution:

The required figure is given below.

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

Line PT is drawn || to line l.

PT is the tangent to the circle.

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