Class 10 Maths Chapter 10 Circles

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CLASS 10 MATHEMATICS

Ch 10 – CIRCLES

Ex 10.1

 1. How many tangents can a circle have?

Answer:

A circle can have infinite tangents to a circle.

We know that A circle is made up of infinite points which are at an equal distance from a point.

So there are infinite points on the Circumference of a circle,

Infinite tangents can be drawn from them.

Chapter 10- figure 3.jpeg

2. Fill in the blanks:

(i) A tangent to a circle intersects it in

…………… point(s).

Answer (i)

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

(ii) A line intersecting a circle in two points

is called a ………….

Answer (ii)

A line intersecting a circle in two points is

called a secant.

(iii) A circle can have …………… parallel

tangents at the most.

Answer: (iii)

A circle can have two parallel tangents at the most.

(iv) The common point of a tangent to a circle

and the circle is called …………

Answer (iv)

The common point of a tangent to a circle and the circle is called the point of contact.

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:

Chapter 10- figure 1.jpeg

In this figure,

the line OP is perpendicular to tangent PQ.

i.e. OP ⊥ PQ

Using Pythagoras theorem in triangle ΔOPQ,

Where Angle P = 90

i.e. (Hypotenuse)2= (base)2+ (perpendicular)2

thus,

OQ2 = OP2+PQ2

(12)= 52+PQ2

144 = 25 + PQ2

PQ2 = 144-25

PQ2 = 119

PQ = √119 cm

Therefore, 

option D i.e. √119 cm is the length of PQ.

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:

Chapter 10- figure 2.jpeg

In the figure,

XY and AB are the two parallel lines.

The line segment AB is the tangent at point C

while the line segment XY is the secant.

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