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Worksheets

Circles (English Medium)

Total questions: 20

Worksheet time: 18mins

Name
Class
Date
1.

The distance between two parallel tangents of a circle of radius 4 cm is

a)

8

b)

6

c)

4

d)

2

2.

A tangent is drawn from a point at a distance of 17 cm of circle C(0, r) of radius 8 cm. The length of its tangent is

a)

23

b)

15

c)

9

d)

5

3.

Two concentric circles of radii a and b (a > b) are given. Find the length of the chord of the larger circle which touches the smaller circle.

a)

a2+b2\sqrt{a^2+b^2}

b)

a2b2\sqrt{a^2-b^2}

c)

2a2b22\sqrt{a^2-b^2}

d)

2a2+b22\sqrt{a^2+b^2}

4.

If TP and TQ are two tangents to a circle with center O such that ∠POQ = 110°, then, ∠PTO is equal to:

a)

700

b)

1100

c)

900

d)

350

5.

In the given figure, AB is a diameter of the circle. If AC = BC, then ∠CAB is equal to

a)

450

b)

300

c)

600

d)

900

6.

In figure, O is the centre of a circle, AB is a chord and AT is the tangent at A. If ∠AOB = 100°, then ∠BAT is equal to

a)

1000

b)

500

c)

400

d)

900

7.

The tangents drawn at the extremities of the diameter of a circle are

a)

perpendicular

b)

equal

c)

parallel

d)

none of these

8.

In the given figure, PA and PB are tangents from a point P to a circle with centre O. Then the quadrilateral OAPB must be a

a)

Square

b)

Rhombus

c)

Parallelogram

d)

Cyclic quadrilateral

9.

TA and TB are the tangents drawn to a circle from an external point T. If  ATB\angle ATB  = 60 then Δ\Delta  TAB is 

a)

Equilateral 

b)

Right Angled 

c)

Obtuse angled 

d)

Isosceles 

10.

A chord of a circle is equal to the radius of the circle, the angle subtended by the chord at a point on the minor arc

a)

900

b)

600

c)

1800

d)

1500

11.

The length of the tangent drawn from a point 8 cm away from the centre of a circle, of radius 6 cm is

a)

5

b)

7\sqrt{7}

c)

1010

d)

10\sqrt{10}

12.

In fig, O is the centre of the circle. PQ is tangent to the circle and secant PAB passes through the centre O. If PQ = 5 cm and PA = 1 cm, then the value of 'x' is

a)

21

b)

12

c)

6

d)

15

13.

In terms of radius, a diameter is equals to

a)

r2r^2

b)

r2\frac{r}{2}

c)

2r

d)

πr\pi r

14.

If two tangents inclined at an angle 60 are drawn to a circle of radius 3 cm then the length of each tangent is

a)

232\sqrt{3}

b)

333\sqrt{3}

c)

4\sqrt{3}

d)

3\sqrt{3}

15.

In the given figure, PT is a tangent drawn from external point P, then the value of OT is

a)

15

b)

12

c)

10

d)

8

16.

In the given figure, AB and AC are tangents to the circle with centre O such that ∠BAC = 40°, then ∠BOC is equal to

a)

400

b)

500

c)

1200

d)

1400

17.

If O is the center of a circle of radius R and AB is a chord of the circle at a distance R/2 from O and OP \perp  AB,  then ∠PBO =

a)

300

b)

450

c)

600

d)

900

18.

The length of tangents drawn from an external point to the circle

a)

perpendicular

b)

equal

c)

parallel

d)

are not defined

19.

In the given figure, if  \angle RPS  = 25°, the value of  ROS\angle ROS  is

a)

135

b)

145

c)

165

d)

155

20.

Both tangent and radii

a)

ordinate from the center of the circle

b)

meet at straight angles

c)

are half a circle's half a circles length

d)

meet a circle at exactly one point