Rajasthan Board RBSE Solutions for Class 10 Maths Chapter 10 Circles Ex 10.1 Textbook Exercise Questions and Answers.

## RBSE Class 10 Maths Solutions Chapter 10 Circles Exercise 10.1

Question 1.

How many tangents can a circle have?

Solution:

We know that one and only one tangent can be drawn at a point of a circle. But circle is the collection of infinitely many points, so we can drawn infinitely many tangents to a circle.

Question 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 ………….. .

Solution:

(i) one

(ii) secant

(iii) two

(iv) 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 PQ is :

(A) 12 cm

(B) 13 cm

(C) 8.5 cm

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

Solution:

Drawing the figure according to the question

OP = 5 cm. and OQ = 12 cm.

∵ PQ is a tangent and OP is a radius

∴ ∠OPQ = 90°

Now, in right △OPQ,

By Pythagoras Theorem,

OQ^{2} = OP^{2} + QP^{2}.

(12)^{2} = (5)^{2} + QP^{2}

QP^{2} = (12)^{2} – (5)^{2}

QP^{2} = 144 – 25 = 119

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

Hence, option (D) is correct.

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:

Let O be the centre of the given circle and PQ be a given line. We are required to draw the lines CD and AD parallel to PQ in which CD is a tangent and AB is a secant.

Construction—

- Draw a perpendicular from centre point to the line PQ which intersects the circle at point C.
- A perpendicular CD has been drawn at point C of radius OC. Here CD is a tangent.
- Draw a perpendicular AB through a point M on OC. Then AB is a secant.

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