Circles Test

Result

Circles Test - 18

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Question 1
1 / -0

There cannot be more than two tangents to a circle parallel to a given secant.

A
True

B
False

C
Either

D
Neither

Solution

Only two parallel tangents are possible to a circle, for a given secant.
Question 2
1 / -0

From an external point, if $$K$$ tangents can be drawn to a circle, then $$K$$ is equal to

A
$$0$$

B
$$2$$

C
$$1$$

D
infinity

Solution

Exactly two tangents can be drawn from an exterior point to a given circle.
So if K tangents are drawn to a circle then K is equal to 2, hence option B is the correct answer.
Question 3
1 / -0

Which of the following is point of contact?

A
$$P$$

B
$$M$$

C
$$O$$

D
$$N$$

Solution

The tangent touches the circle at point of contact.
Here, P is the point of contact.
So, option A is correct.
Question 4
1 / -0

In the following figure, PQ and PR are tangents to a circle with center O. Line segment AC touches the circle at point B, then state the relation between the tangents PQ and PR.

A
$$PQ=PR$$

B
$$PQ<PR$$

C
$$PQ>PR$$

D
Cannot be determined

Solution

We know that the length of the tangents to a circle, drawn from a point, are equal.
$$\therefore PQ=PR$$.
Correct option is $$A$$
Question 5
1 / -0

A tangent to a circle is a line that intersects the circle in only one point.

A
True

B
False

C
Either

D
Neither

Solution

Line that intersects the circle in only 1 point, i.e. which touches the circle at a point is a tangent.
Question 6
1 / -0

A circle is entirely in another circle. then which of the following is correct ?

A
only one common tangent

B
two common tangents

C
no common tangent

D
infinite number of tangents

Solution

If one circle is completely inside another circle, then there can not be drawn any common tangents.
Question 7
1 / -0

A circle can have at the most two parallel tangents.

A
True

B
False

C
Either

D
Neither

Solution

Only two parallel tangents are possible for a circle.
Question 8
1 / -0

The maximum number of common tangents drawn to two intersecting circles at two points is

A
$$1$$

B
$$2$$

C
$$3$$

D
$$4$$

Solution

Consider the two intersecting circle.
In this case the maximum number of common tangent drawn to intersecting circle is $$2$$.
Hence, this is the answer.
Question 9
1 / -0

A secant intersects the circle at _______ points.

A
$$0$$

B
$$1$$

C
$$2$$

D
$$3$$

Solution

Secant is a line that intersects the circle at $$2$$ points. In the above figure, $$AB$$ is a secant of the circle which intersect it at points $$A$$ and $$B.$$
Question 10
1 / -0

The number of tangents that can be drawn to a circle at a given point on it is

A
one

B
two

C
three

D
none of these

Solution

Consider a circle,

The number of tangents that can be drawn to a circle at a given point on it is one