Number of Tangents Drawn from a Given Point

Q. The number of tangents that can be drawn at a point on the circle is

1. 0
2. 1
3. 2
4. Infinite

Q.

In a circle of radius 7cm, tangent PT is drawn from point P such that PT= 24cm. If O is the centre of the circle, then the length of OP is:

1. 31cm

2. 25cm

3. 30cm

4. 28cm

Q.

Two circles touch each other externally.

Prove that the tangents drawn to the two circles from any point on the common tangent are equal in length. [2 MARKS]

Q.

Which lines are tangent to the circle Why?

Q. How many tangents can be drawn from a point inside circle

1. 2
2. infinitely many
3. one
4. 0

Q. How many tangents can be drawn from a point outside the circle?

1. 1
2. 2
3. 3
4. 0

Q. 63. Two straight lines rotate about two fixed points (-a, 0)and (a, 0) in antic clockwise direction. If they start fromtheir position of coincidence such that one rotates at arate double of the other, then locus of curve is

Q. 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.

1. $0$
2. $1$
3. $2$
4. $3$

Q. How many tangents lines can be drawn to a circle from a point outside the circle ?

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

Q. In the figure, seg $AB$ and seg $AD$ are tangent segments drawn to a circle with centre $C$ from exterior point $A$, then prove that:
$\begin{array}{cc}\angle A=\frac{1}{2}& \left[m\right(\mathrm{arc}BBP)\\ -m\left(\mathrm{arc}BXD\right)]& \end{array}$

Q.

Prove that the lengths of the tangents drawn from an external point to a circle are equal. Using the above, do the following:

In the fig., XP and XQ are tangents from T to the circle with centre O and R is any point on the circle. If AB is a tangent to the circle at R, prove that XA +AR = XB + BR

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

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

Q.

Prove that the tangents at the extremities of any chord make equal angles with the chord.

Q. Maximum number of tangents that can be drawn from an external point to a circle is ______ .

Q. Which of the following statements are true?
1) No tangents can be drawn to a circle from an interior point.
2) Only two tangents, at most, can be drawn to a circle from an exterior point.

1. Both 1 and 2
2. Neither 1 nor 2
3. Only 1
4. Only 2

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

1. $2$
2. $3$
3. $4$
4. $0$

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

1. one
2. two
3. three
4. none of these

Q.

In the given figure, a line intersects a circle at two points A and B. Now a point P, as shown in the figure, is fixed and the line is rotated about P in both directions until the points A and B coincide. How many times will they coincide?

1. 1

2. 2

3. 0

4. Infinite

Q.

Assertion (A) in the given figure, O is the centre of the circle with D, E and F as mid-points of AB, BO and OA respectively. If $\angle DEF$ is ${30}^{\circ }$, then $\angle ACB$ is ${60}^{\circ }$

Reason (R) Angle subtended by an arc at the centre is twice the angle subtended by it on the remaining part of the circle.
which of the following is true?

1. (A) is true and (R) is the correct explanation of (A)

2. (A) is false and (R) is the correct explanation of (A)

3. A is true and (R) is false

4. Both (A) and (R) are false

Q.

In fig. XP and XQ are tangents from X to the circle with center O. R is a point on the circle. Prove that, XA + AR = XB + BR. [2 MARKS]

Q. How many tangents can be drawn on the circle of radius $5\text{cm}$ from a point lying outside the circle at distance $9\text{cm}$ from the center.

Q. If two circles touch each other externally, then the total number of their common tangent(s) is/are

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

Q.

$\text{If AB is the tangent to the circle with}\text{center O then, find the measure of}\angle OCP.$
$\text{Given that OP = PC.}$

1. ${30}^{\circ }$

2. ${45}^{\circ }$

3. ${60}^{\circ }$

4. ${15}^{\circ }$

Q. 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

1. $2$
2. $1$
3. $0$
4. $3$

Q. 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 $2$

1. $0$
2. $1$
3. $2$
4. $3$

Q. Two tangents PA and PB are drawn to a circle with centre O, such that $\angle APB={120}^{\circ }$ Prove that $OP=AP+BP=2AP$

Q. 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 $C_2$

1. $P_3$
2. $P_1$
3. $P_4$
4. $P_5$

Q. If two circles touch externally, then number of common tangents is

1. $2$
2. $3$
3. $1$
4. $0$

Q. How many common tangents can be drawn?

1. $0$
2. $1$
3. $2$
4. $3$

Q.

Prove that the circle drawn with any side of a rhombus as diameter, passes through the point of intersection of its diagonals.