Tangent

Q.

In the given diagram O is the center of the circle and CD is a tangent. $\angle$CAB and $\angle$ACD are supplementary to each other $\angle$OAC = ${30}^{\circ }$. Find the value of $\angle$OCB:

1. None of these

2. 30°

3. 20°

4. 60°

Q.

A line that intersects a circle in exactly one point is called a __________ .

1. diameter
2. secant
3. radius
4. tangent

Q.

If the length of the chord of the circle: $x^2+y^2=r^2\left(r>0\right)$ along the line $y-2x=3$ is $r$, then $r^2$ is equal to

1. $12$

2. $\frac{24}{5}$

3. $\frac{9}{5}$

4. $\frac{12}{5}$

Q.

PAQ is a tangent to the circle with center O at a point A as shown in figure. If $\angle OBA={35}^{\circ }$, find the value of $\angle BAQ$ and $\angle ACB$. [4 MARKS]

Q. If there is exactly one point common to a line AB and a circle, then the line AB can be

1. A secant
2. A tangent to the circle
3. Sometimes a secant and sometimes a tangent
4. A chord of the circle

Q.

A bucket is raised from a well by means of a rope, which is wound round a wheel of diameter 77 cm. Given that the bucket ascends in 1 min 28 seconds with a uniform speed of 1.1 m/s, calculate the number of complete revolutions the wheel makes in raising the bucket.

1. 20

2. 40

3. 80

4. 50

5. 400

Q. Two tangent segment PA and PB are drawn to a circle center O such that angle APB = 120. Prove that OP = 2 AP.

Q. How many tangents can be drawn to a circle through an external point?

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

Q. The point where the tangent touches the circle is called ___.

1. Midpoint
2. Centre of the circle
3. Point of inflection
4. Point of contact

Q. Which of the following line segments represents the radius of the given circle?

1. OA
2. PQ
3. MN
4. None of these

Q. In figure, AT is a tangent to the circle with centre O such that OT = 4 cm and $\angle OTA={30}^{\circ }$ . Then , AT is equal to

Q. The region enclosed between two radii and the corresponding arc in a circle is called a________ of the circle.

1. segment
2. arc
3. sector
4. circumference

Q.

A garden roller has a circumference of 4 m. The number of revolutions it makes in moving 40 metres are:

1. 16

2. 12

3. 8

4. 10

Q.

How many tangents can be drawn to a circle from a point in its interior?

1. None

2. Infinite

3. Two

4. One

Q.

Which of the following points lies on the tangent to the curve ${\mathrm{x}}^4{\mathrm{e}}^{\mathrm{y}}+2\sqrt{(\mathrm{y}+1)}=3$ at the point $\left(1,0\right)$?

1. $\left(2,6\right)$

2. $\left(2,2\right)$

3. $\left(-2,6\right)$

4. $\left(-2,4\right)$

Q. From a point Q, 13 cm away from the centre of a circle, the length of tangent PQ to the circle is 12 cm. The radius of the circle (in cm) is
(a) 25
(b) $\sqrt{313}$
(c) 5
(d) 1

Q.

which of the following pairs of lines in a circle cannot be parallel ?

(a) Two chords (b) A chord and a tangent

(c) Two tangents (d) Two diameters

Q.

Which of the following statements is not true ?

(a) A tangent to a circle intersects the circle exactly at one point.

(b) The point common to the circle and its tangent is called the point of contact.

(c) The tangent at any point of a cricle is perpendicular to the radius of the circle through the point of contact.

(d) A straight line can meet a circle at one point only.

Q.

Prove that a line drawn through the end point of a radius and perpendicular to it is a tangent to the circle.

Q.

The condition for a line $y=2x+c$ to touch the circle $x^2+y^2=16$ is

1. $c=10$

2. $c^2=80$

3. $c=12$

4. $c^2=64$

Q. is a line that touches a circle at only one point, and is a line that intersects a circle at two distinct points.

1. Arc
2. Tangent
3. secant
4. sector

Q.

State True or False.

PA and PB are tangents to the circle with centre O from an external point P, touching the circle at A and B respectively. Then the quadrilateral AOBP is cyclic.

1. Point of contact

2. Point of secant

Q.

In Fig., if $AB=AC$, prove that $BE=EC$ [2 MARKS]

Q. Find the greatest possible length which can be used to measure exactly the lengths $7$ m$,3$ m$,85$ m$,12$ m $95$ cm.

Q.

A line that intersects a circle at two points is called a

___.

Q. How many circles can be drawn passing through three definite points when they are non collinear?

Q.

How many intersection points can a line have with a circle depending on its position?

1. 0 or 1

2. 1

3. 2

4. 0, 1 or 2

Q.

O is the centre of the circle and line XY shares one common point with the circle. A line segment OP is drawn from O to line XY such that P is a point on line XY. What happens if P lies on the circle?

1. This situation holds no signifiance

2. OP need not be radius of circle

3. OP is perpendicular to XY

4. The angle between OP and XY is variable

Q. Which of the given line segments is a diameter of the given circle?

1. OA
2. PQ
3. MN
4. None of these

Q. Consider the following statement :
I. Two circles with centres A and B, radii 3 cm and 4 cm respectively intersect at two points C and D.
II. AC and BC are tangents to the two circles.
Then, length of chord CD will be___.
Choose the correct option.

1. Statement II alone is sufficient to answer
2. Statement I alone is sufficient to answer
3. Neither of the statement is sufficient.
4. Both statements are required to answer