Circles Test

Result

Circles Test - 24

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Question 1
1 / -0

How many common tangents can be drawn?

A
$$0$$

B
$$2$$

C
$$3$$

D
$$4$$

Solution

$$4$$ common tangents can be drawn asshown in the figure.
So, option D is correct.
Question 2
1 / -0

How many common tangents can be drawn to the circles in the figure?

A
$$0$$

B
$$1$$

C
$$2$$

D
$$3$$

Solution

If two circles are intersecting, then two common tangents can be drawn.

So, option $$C$$ is correct.
Question 3
1 / -0

If $$P$$ is a point, then how many tangents to a circle can be drawn from the point $$P$$, if it lies Inside the circle.

A
$$0$$

B
$$1$$

C
$$2$$

D
$$3$$

Solution

There is no tangent to the circle through a point lying inside the circle.
Question 4
1 / -0

If $$P$$ is a point, then how many tangents to a circle can be drawn from the point $$P$$, if it lies outside the circle

A
$$0$$

B
$$1$$

C
$$2$$

D
$$3$$

Solution

There are exactly 2 tangents to a circle through a point lying outside the circle.
Question 5
1 / -0

Which of the following is secant to the circle given above?

A
Pc

B
CD

C
C

D
PQ

Solution

$$AB$$ is chord. $$CD$$ is diameter. Line at $$C$$ is tangent.
So, $$PQ$$ is a secant to the circle given.
A line through two points on a circle is called a secant.
Question 6
1 / -0

In given figure $$C_1$$ and $$C_2$$ are two circles and points $$P_1,\,P_2,\,P_3,\,P_4,\,P_5$$ are noted. Which one is greater: no of tangents possible to $$C_1$$ from $$P_3$$ or $$C_2$$ from $$P_3$$

A
To $$C_1$$

B
To $$C_2$$

C
Both are same

D
No tangents

Solution

From $$P_3$$ one tangent is possible to $$C_2$$ and no tangent is possible to $$C_1$$.
Question 7
1 / -0

In given figure $$C_1$$ and $$C_2$$ are two circles and points $$P_1,\,P_2,\,P_3,\,P_4,\,P_5$$ are noted. From which point no tangent is possible to both $$C_1$$ and $$C_2$$

A
$$P_1$$

B
$$P_3$$

C
$$P_4$$

D
$$P_5$$

Solution

Points that lie in the interior of a circle cannot be used to draw tangents to that circle.
Hence, $$P_5$$ is a point common to both circles from which no tangent can be drawn.
Question 8
1 / -0

From a point inside the circle how many secants can be drawn to the circle?

A
$$0$$

B
$$1$$

C
$$2$$

D
Infinite

Solution

From a point P inside the circle, infinite number of secants can be drawn.
So, option D is correct.
Question 9
1 / -0

From an outside point how many secants can be drawn to the circle?

A
$$0$$

B
$$1$$

C
$$2$$

D
Infinite

Solution

From a point outside the circle, infinite secants can be drawn to the circle.
Question 10
1 / -0

In given figure $$C_1$$ and $$C_2$$ are two circles and points $$P_1,\,P_2,\,P_3,\,P_4,\,P_5$$ are noted. How many points are there from which no. of tangents drawn to $$C_2$$ are $$2$$

A
$$0$$

B
$$1$$

C
$$2$$

D
$$3$$

Solution

All the points that lie in the exterior of $$C_2$$ can be used to draw 2 tangents each to it.
Hence, $$P_1, P_2$$ and $$P_4$$ i.e. 3 points.