Circles Test

Result

Circles Test - 25

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Question 1
1 / -0

If a circle is inside another circle, then what is the maximum number of tangents from any point on the outer circle to the inner circle?

A
$$0$$

B
$$1$$

C
$$2$$

D
$$3$$

Solution

From the given condition, only 2 tangents can be drawn.
Hence, option C is correct.
Question 2
1 / -0

There are two circles with centres $$c_1\;\&\;c_2$$ with having radii $$3\;cm$$. Distance between their centres is $$8\;cm$$
How many common tangents can be drawn?

A
$$2$$

B
$$3$$

C
$$4$$

D
$$0$$

Solution

4 common tangents can be drawn to the given circles.
So, option C is correct.
Question 3
1 / -0

A nickel is placed on a table. The number of nickels which can be placed around it, each tangent to it and to two others is:

A
$$4$$

B
$$5$$

C
$$6$$

D
$$8$$

Solution

Around a given circle, there can be placed exactly six circles each equal to the even circle, tangent to it, and tangent to two others.
These are between two successive points of contact of the given circle and the outside circle is one sixth of the circumference.
So the number of pins will be $$6$$.
Question 4
1 / -0

The maximum number of tangents which can be drawn from an external point to a circle are.

A
$$1$$

B
$$3$$

C
Infinite

D
$$2$$

Solution

If the point lies inside the circle no tangent can be drawn.
If the point lies on the circle then only one tangent can be drawn
If the point lies outside the circle then maximum two tangent lines can be drawn on the circle
Question 5
1 / -0

Select the correct statements for a tangent of a circle:

P: Tangent intersects circle in one & only one point.
Q: Tangent and circle must be in same plane.
R: Tangent passes through the centre of a circle.

A
$$Q$$ and $$R$$

B
Only $$Q$$

C
Only $$P$$

D
$$P$$ and $$Q$$

Solution

Both the statements $$P$$ and $$Q$$ are correct for a tangent.
Tangent intersects the circle in one and only one point.
Tangent and the circle must be in same plane.

Hence, $$Op-D$$ is correct .
Question 6
1 / -0

In the figure, $$AB$$ is called .........

A
secant

B
tangent

C
chord

D
none

Solution

The line that crosses the circles at two points is known as secant.
So AB is secant.
Question 7
1 / -0

The number of tangents that can be drawn to a circle at a point on the circle is:

A
$$ 3 $$

B
$$ 2 $$

C
$$ 1 $$

D
$$ 0 $$

Solution

$${\textbf{Step -1: Let a circle with centre O and a point P on the circle and make a line }}\mathbf{\left( {{\text{say m}}} \right)}$$
$${\textbf{ perpendicular to radius OP.}}$$

$${\textbf{Step -2: Now take any point Q on the line m,}}$$

$${\text{We can say that }}OP{\text{ }} < {\text{ }}OQ{\text{ since }}OQ{\text{ is the hypotenuse of }}\Delta OPQ{\text{.}}$$
$${\text{We can say that Q is an exterior point and lie outside the circle and this will be true for all points}}$$
$${\text{lying on line}}\left( {\text{m}} \right){\text{ except the point P lying on circle}}{\text{.}}$$

$${\text{Since line}}\left( {\text{m}} \right){\text{ touches the circle at a single point, we can say that tangent at any}}$$
$${\text{ point of a circle is unique}}{\text{.}}$$

$${\textbf{Hence, Only one tangent can be drawn to a circle from a point on the same circle}}{\text{.}}$$
Question 8
1 / -0

A straight line which passes through two points on a circle is

A
A chord

B
A secant

C
A tangent

D
The radius

Solution

A straight line which passes through two points on a circle is a secant.
Question 9
1 / -0

How many tangents can be drawn from the point inside of the circle to the that circle?

A
$$1$$

B
$$2$$

C
$$3$$

D
None of these

Solution

No tangent can be drawn from the point inside of a circle to that circle.
Question 10
1 / -0

The maximum number of tangents that can be drawn to a circle from a point outside the circle is___

A
$$ 2 $$

B
$$ 1 $$

C
$$ 0 $$

D
Uncountable

Solution

The maximum number of tangents that can be drawn to a circle from a point outside the circle is $$ 2 $$ .

Hence, the correct option is $$A$$.