Relation between a Line and The Circle

Q. In the given figure, which of the following is Secant?

1. $AB$
2. $BC$
3. $DE$
4. None

Q. A tangent line passes through the center of the circle

1. False
2. True

Q. A tangent of length $12\text{cm}$ is drawn to the circle of radius $5$ cm from point $A$. Find out the distance between the point $A$ and the centre of the circle.

1. $13$ cm
2. $14$ cm
3. $17$ cm
4. $15$ cm

Q. The maximum possible number of points of intersection of a line and circle is

1. $1$
2. $2$
3. $3$
4. $4$

Q. We have a circle of diameter $100cm$. What is the maximum number of tangents that can be drawn for this circle?

1. $100$
2. Infinite
3. $1000$
4. (a) and (c) above.

Q. Which of the following statement(s) is/are true?
$P:$ A tangent to a circle cut the circle at one point.
$Q:$ Chord is a line segment made up of tangent line.
$R:$ Secant line intersects the circle at $2$ points.

1. $P,Q$
2. $Q,R$
3. $P,R$
4. $P,Q,R$

Q. If the diameter of this circle is 10 cm, find the length of the chord AB.

Q. Which of the following statements given below are correct?

1. A tangent touches a circle at only one point.
2. End points of a chord lies on the circle.
3. Secants are the line segments which cut the circle at two distinct points.

1. $1$ and $2$ Only
2. $3$ and $3$ Only
3. $1$ and $3$ Only
4. $1$, $2$ and $3$ all correct.

Q. Sort the following lines in ascending order based on the number of points it intersects the circle with.

1. Tangent < Secant < No Intersection
2. Secant < Tangent < No Intersection
3. No Intersection < Secant < Tangent
4. No Intersection < Tangent < Secant

Q.
In the above figure, $PC$ is the tangent and $BC$ is the diameter of circle where $O$ is centre of the circle. A secant from point $P$ is drawn that cut the circle at point $A$ and $B$ such that $AB$ is equal to radius of the circle. find $\angle P$.

1. ${30}^o$
2. ${60}^o$
3. ${45}^o$
4. ${35}^o$

Q. Identify the tangent, chord, secant and no-intersection for the following circle.

1. Tangent - $AB$, Chord - $JK$, Secant - $CD$ and no-intersection - $LM$
2. Tangent - $EF$, Chord - $GI$, Secant - $JK$ and no-intersection - $LM$
3. Tangent - $EF$, Chord - $GH$, Secant - $GI$ and no-intersection - $LM$
4. Tangent - $LM$, Chord - $JK$, Secant - $CD$ and no-intersection - $CD$

Q. Two tangents are drawn to the circle at an angle of ${60}^o$ what is the length of each tangent if chord toching the point of contacts of both the tangents is $6$ cm?

1. $3\sqrt{3}$ cm
2. $6$ cm
3. $6\sqrt{3}$ cm
4. $3$ cm

Q. Which of the following is correct for the circle given below?

1. $AC$ is a tangent
2. $AB$ is a secant
3. $AC$ is a secant
4. $AB$ is a tangent