Students can Download Class 10 Maths Chapter 4 Circles Ex 4.1 Questions and Answers, Notes Pdf, KSEEB Solutions for Class 10 Maths helps you to revise the complete Karnataka State Board Syllabus and to clear all their doubts, score well in final exams.

## Karnataka State Syllabus Class 10 Maths Chapter 4 Circles Ex 4.1

Question 1.

How many tangents can a circle have?

Answer:

There is only one tangent at a point of the circle.

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 _____________ .

Answers:

- one
- tangent
- 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 PQ is.:

a) 12 cm.

b) 13 cm.

c) 8.5 cm.

d) √119 cm.

Answer:

d) √119 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

\(\therefore \sqrt{\mathrm{PQ}^{2}}=\sqrt{119}\)

\(\therefore \mathrm{PQ}=\sqrt{119} \mathrm{cm}\)

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.

Answer:

CD is the tangent parallel to AB.

AB is secant, it meets RS at P.