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

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 :

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

Solution:

1. exactly one
2. secant
3. two
4. 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.