In this chapter, we provide KSEEB SSLC Class 10 Maths Solutions Chapter 4 Circles Ex 4.1 for English medium students, Which will very helpful for every student in their exams. Students can download the latest KSEEB SSLC Class 10 Maths Solutions CChapter 4 Circles Ex 4.1 pdf, free KSEEB SSLC Class 10 Maths Solutions Chapter 4 Circles Ex 4.1 book pdf download. Now you will get step by step solution to each question.

**Karnataka State Syllabus Class 10 Maths Solutions Chapter 4 Circles Ex 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 :

- 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) 19 cm.

Solution:

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

∴ √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:

CD is the tangent parallel to AB.

AB is secant, it meets RS at P.

**All Chapter KSEEB Solutions For Class 10 Maths**

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