**KSEEB SSLC Class 10 Maths Solutions Chapter 4 Circles Ex 4.1** are part of KSEEB SSLC Class 10 Maths Solutions. Here we have given Karnataka SSLC Class 10 Maths Solutions Chapter 4 Circles Exercise 4.1.

## Karnataka SSLC Class 10 Maths Solutions Chapter 4 Circles Exercise 4.1

Question 1.

How many tangents can a circle have?

Solution:

There is only one tangent at a point of the 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) Exactly 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) 19 cm.

Solution:

d) \(\sqrt{119} \mathrm{cm}\).

A tangent PQ at a point P of a circle.

OP is the radius drawn from centre of the circle to the tangent.

∴ OP ⊥ PQ.

Now, in ⊥ ∆OPQ, ∠P = 90°

∴ As per Pythagoras theorem,

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

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

25 + PQ^{2} = 144

PQ^{2} = 144 – 25

PQ^{2} = 119

∴ √PQ^{2 } = √119

∴ PQ = √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:

We have the required figure, as shown

We hope the given KSEEB SSLC Class 10 Maths Solutions Chapter 4 Circles Ex 4.1 will help you. If you have any query regarding Karnataka SSLC Class 10 Maths Solutions Chapter 4 Circles Exercise 4.1, drop a comment below and we will get back to you at the earliest.