# PSEB Solutions for Class 10 Maths Chapter 10 Circles Ex 10.1

PSEB Solutions for Class 10 Maths Chapter 10 Circles Ex 10.1

## PSEB 10th Class Maths Solutions Chapter 10 Circles Ex 10.1

Question 1.

How many tangents can a circle have?

Solution:

Since at any point on a circle, there can be one and only one tangeni. But circle is a collection of infinite points, so we can draw infinite number of tangents to a circle.

Question 2.

Fill in the blanks:

(i) A tangent to a circle intersects it in ………………. point(s).

Solution:

one

(ii) A line intersecting a circle in two points is called a ………………..

Solution:

secant.

(iii) A circle can have ……………. parallel tangents at the most.

Solution:

two

(iv) The common point of a lingent h, circle and the circit is called ………………

Solution:

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) √119 cm.

Solution:

According to given information we draw the figure such that,

OP = 5 cm and OQ = 12 cm

∵ PQ is a tangent and OP is the radius

∵ ∠OPQ = 90°

Now, In right angled ∆OPQ.

By Pythagoras Theorem,

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

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

Or QP^{2} = (12)^{2} – (5)^{2}

Or QP^{2} = 144 – 25 = 119

Or QP = √119 cm.

Hence, option (D) is correct.

Question 4.

Draw a circle and two lines parallel to given line such that one is a tangent and other a secant to the circle.

Solution:

According to thc given information we draw a circle having O as centre and l is the given line.

Now, m and n be two lines parallel to a given line l such that m is tangent as well as parallel to l and n is secant to the circle as well as parallel to l.

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