Circles Test

Result

Circles Test - 17

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Weekly Quiz Competition

Question 1
1 / -0

The maximum number of common tangents that can be drawn to two circles intersecting at two distinct points is

A
1

B
2

C
3

D
4

Solution

only two common tangents are possible
because circles intersect at two points.
Question 2
1 / -0

There is only one tangent at any point on the circumference of a circle.
Say true or false.

A
True

B
False

C
Ambiguous

D
Data insufficient

Solution

Only one tangent possible at a point on the circumference of a circle.
Question 3
1 / -0

If the angle between two radii of a circle is $$100^{\circ}$$, the angle between the tangents at the ends of those radii is :

A
$$50^{\circ}$$

B
$$60^{\circ}$$

C
$$80^{\circ}$$

D
$$90^{\circ}$$

Solution

From the figure, it is evident that $$\angle AOB = 100^{\circ}$$.
Now, $$\angle OAP = 90^{\circ}$$ and $$\angle OBP = 90^{\circ}$$ (radii is perpendicular to tangent at point of contact)
Also, sum of interior angles of a quadrilateral is $$360^{\circ}$$ and hence,
$$\angle APB = 360^{\circ} - \angle OAP - \angle OBP -\angle AOB=80^{\circ}$$
This is the required angle between the tangents.
Question 4
1 / -0

There is no tangent to a circle passing through a point lying ..... the circle.

A
inside

B
outside

C
on the circle

D
none of these

Solution

Tangent touches the circle at one point only and so it is not possible for a point inside a circle.
Question 5
1 / -0

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

A
Point of contact

B
Tangent

C
Chord

D
Diameter

Solution

The point where tangent touches the circle is called point of contact.
Question 6
1 / -0

A line that intersects a circle at two distinct points is called

A
a diameter

B
a secant

C
a tangent

D
a radius

Solution

A line which intersects a circle at two distinct points is called a secant.
So option B is the right answer.
Question 7
1 / -0

How many parallel tangents can a circle have?

A
1

B
2

C
Infinite

D
None of these

Solution

A circle can have exactly two parallel tangents and they must pass through ends of a diameter. That is their point of contacts must be diametrically opposite.
So option B is the correct answer.
Question 8
1 / -0

The length of tangent drawn from a point $$8\ cm$$ away from centre of circle of radius $$6\ cm$$ is :

A
$$\sqrt{5} cm$$

B
$$2\sqrt{5} cm$$

C

$$5\ cm$$

D
$$2\sqrt{7} cm$$
Question 9
1 / -0

There are exactly two tangents to a circle passing through a point lying ____ the circle.

A
Inside

B
Outside

C
On the circle

D
None of the Above

Solution

For a point outside a circle, two tangents can be drawn to the circle.
Question 10
1 / -0

A line intersecting a circle in two points is called a .....

A
Chord

B
Secant

C
Tangent

D
Radius

Solution

$$\textbf{Step -1: Analysing the given multiple choice.}$$
$$\text{From the following multiple-choice questions, }$$
$$\text{A chord is a line segment that joins any two points on the circumference of the circle.}$$
$$\text{A secant is a line that passes through any two points on the circumference of the circle.}$$
$$\text{Whereas a tangent is a line that touches the circle at a single point.}$$
$$\text{Radius is the distance between the center and any point on the circumference.}$$
$$\textbf{Hence, a line intersecting a circle in two points is called a secant. Thus, option B is correct.}$$

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Re-Attempt Weekly Quiz Competition

Circles Test - 17

Result

Circles Test - 17

Score

-

Rank

-

SHARING IS CARING

Question 1

1

2

3

4

Solution

Question 2

True

False

Ambiguous

Data insufficient

Solution

Question 3

$$50^{\circ}$$

$$60^{\circ}$$

$$80^{\circ}$$

$$90^{\circ}$$

Solution

Question 4

inside

outside

on the circle

none of these

Solution

Question 5

Point of contact

Tangent

Chord

Diameter

Solution

Question 6

a diameter

a secant

a tangent

a radius

Solution

Question 7

1

2

Infinite

None of these

Solution

Question 8

$$\sqrt{5} cm$$

$$2\sqrt{5} cm$$

$$5\ cm$$

$$2\sqrt{7} cm$$

Question 9

Inside

Outside

On the circle

None of the Above

Solution

Question 10

Chord

Secant

Tangent

Radius

Solution

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