Free Printable Height & Distance and Circle

1.

A line intersecting a circle in two distinct points is called

a)

Tangent

b)

Secant

c)

Centre

d)

Radius

2.

In the figure, PA and PB are tangents to a circle with centre O. If $\angle AOB=120\degree$ then what is $\angle OPA$

a)

$30\degree$

b)

$80\degree$

c)

$90\degree$

d)

$25\degree$

3.

In the figure if AP and BP are the two tangents to a circle with centre O so that $\angle AOB=110\degree$ , then $\angle APB$ is equal to

a)

$60\degree$

b)

$70\degree$

c)

$80\degree$

d)

$90\degree$

4.

The length of tangent from a point A at a distance of 5 cm from the centre of the circle is 4 cm. What is the radius of the circle?

a)

2 cm

b)

3 cm

c)

4 cm

d)

5 cm

5.

From the figure from a point P which is at a distance 13 cm from the centre O of a circle of radius 5 cm , the pair of tangents AP and BP to the circle are drawn. Then the area of the quadrilateral PAOB is

a)

$40\ cm^2$

b)

$50\ cm^2$

c)

$60\ cm^2$

d)

$30\ cm^2$

6.

Two concentric circles are of radii 6.5 cm and 2.5 cm. Find the length of the chord of the larger circle which touches the smaller circle

a)

10 cm

b)

12 cm

c)

11 cm

d)

7 cm

7.

What is the value of x if both segments are tangent to the circle?

a)

A

b)

B

c)

C

d)

D

8.

An observer 1.5 metres tall is 20.5 metres away from a tower 22 metres high. Determine the angle of elevation of the top of the tower from the eye of the observer.

a)

0⁰

b)

30⁰

c)

45⁰

d)

60⁰

9.

A spherical balloon of radius r subtends an angle θ at the eye of an observer. If the angle of elevation of its centre is φ, then the height of the centre of the balloon is :

a)

r tan φ cosec θ/2

b)

r sin φ cosec θ/2

c)

r sin φ tan θ/2

d)

r cosec φ sin θ/2

10.

From a balloon vertically above a straight road, the angles of depression of two cars at an instant are found to be 45° and 60°. If the cars are 100 m apart, then the height of the balloon is

a)

$50\left(2+\sqrt{3}\right)$ m

b)

$100\left(3+\sqrt{3}\right)$ m

c)

$100\left(2+\sqrt{3}\right)$ m

d)

$50\left(3+\sqrt{3}\right)$ m

11.

The shadow of a tower standing on a level plane is found to be 50 m longer when Sun’s elevation is 30° than when it is 60°. The height of the tower is :

a)

$\frac{25}{\sqrt{3}}$ m

b)

$15\sqrt{3}$ m

c)

$25\sqrt{3}$ m

d)

$20\sqrt{3}$ m

12.

From the top of a tower h m high, the angles of depression of two objects, which are in line with the foot of the tower are α and β (β > α). Then the distance between the two objects is :

a)

$h\left(\tan\beta-\tan\propto\right)$

b)

$h\left(\tan\propto-\tan\beta\right)$

c)

$h\left(\cot\beta-\cot\propto\right)$

d)

$h\left(\cot\propto-\cot\beta\right)$

13.

The angle of elevation of the top of a vertical tower from a point on the ground is $60\degree$ . From another point 10 m vertically above the first, its angle of elevation is $45\degree$ , then the height of the tower.is :

a)

$5\left(\sqrt{3}+3\right)$ m

b)

$5\left(\sqrt{3}+2\right)$ m

c)

$5\left(\sqrt{3}+4\right)$ m

d)

$5\left(2\sqrt{3}+3\right)$ m

14.

The lower window of a house is at a height of 2 m above the ground and its upper window is 4 m vertically above the lower window. At certain instant the angles of elevation of a balloon from these windows are observed to be $60\degree$ and $30\degree$ ,respectively. Find the height of the balloon above the ground.

a)

6 m

b)

7 m

c)

8 m

d)

9 m

15.

A window of a house is h metres above the ground. From the window, the angles of elevation and depression of the top and the bottom of another house situated on the opposite side of the lane are found to be α and β, respectively. Then the height of the other house is :

a)

h ( 1 + sin β cos α ) metres.

b)

h ( 1 + tan β cot α ) metres.

c)

h ( 1 + sinn α cos β ) metres.

d)

h ( 1 + tan α cot β ) metres.

16.

At one end A of a diameter AB of a circle of radius 5 cm, tangent XAY is drawn to the circle. The length of the chord CD parallel to XY and at a distance 8 cm from A is

a)

4 cm

b)

5 cm

c)

6 cm

d)

8 cm

17.

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

a)

$\frac{\left(3\sqrt{3}\right)}{2}$ cm

b)

6 cm

c)

3 cm

d)

$3\sqrt{3}$ cm

18.

A is a point at a distance 13 cm from the centre O of a circle of radius 5 cm. AP and AQ are the tangents to the circle at P and Q. If a tangent BC is drawn at a point R lying on the minor arc PQ to intersect AP at B and AQ at

C, then the perimeter of the ∆ABC is :

a)

25 cm

b)

20 cm

c)

24 cm

d)

30 cm

19.

If an isosceles triangle ABC, in which AB = AC = 6 cm, is inscribed in a circle of radius 9 cm, then the area of the triangle is :

a)

$8\sqrt{2}cm^2$

b)

$10\sqrt{2}cm^2$

c)

$8\sqrt{3}cm^2$

d)

$10\sqrt{2}cm^2$

20.

O is the centre of a circle of radius 5 cm, T is a point such that OT = 13 cm and OT intersects the circle at E. If AB is the tangent to the circle at E, then the length of AB is

a)

8 cm

b)

22/3 cm

c)

7 cm

d)

20/3 cm

Height & Distance and Circle

Total questions: 20

Worksheet time: 40mins

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