Tangent as Special Case of Secant

Q.

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

1. Tangent

2. Radius

3. Chord

4. Diameter

Q.

If two tangents inclined at an angle of ${60}^{\circ },$ are drawn to a circle of radius $3cm$, the length of each tangent is equal to:

1. $3$

2. $6$

3. $\left(\frac{3}{2}\right)\sqrt{3}$

4. $3\sqrt{3}$

Q.

In a triangle ABC, $\angle A={60}^{\circ }$ and the incircle (centre O) touches BC, CA and AB at points P, Q and R respectively.

1. $\angle QOR={120}^{\circ }$

2. $\angle QPR={60}^{\circ }$

3. $\angle QOR={90}^{\circ }$

4. $\angle QPR={50}^{\circ }$

Q. The chord that passes through the centre of a circle is called the radius.

1. False
2. True

Q. If radii of two circles are $4cm$ and $2.8cm$ which touches externally, then find the distance between their centres.

Q.

The radius of a circle is 8 cm. Calculate the length of a tangent drawn to this circle from a point at a distance of 10 cm from its centre.

1. 9 cm

2. 7 cm

3. 2 cm

4. 6 cm

Q. 𝐀𝐏 is the tangent to the circle with centre 𝐎 and radius 𝟖 𝐜𝐦. If 𝐀𝐁 = 𝟗 𝐜𝐦, then the length of the tangent 𝐀𝐏 is?

Q. Fill in the blanks:

(i) The common point of a tangent and the circle is called ..........

(ii) A circle may have .............. parallel tangents.

(iii) A tangent to a circle intersects in it ............ point(s).

(iv) A line intersecting a circle in two points is called a ...........

(v) The angle between tangent at a point on a circle and the radius through the point is ........

Q.

A secant which meets the circle at A and B is dragged up until A, B concide at a point. What is that point called?

1. Point of secant

2. Point of contact

3. End Point of secant

4. Tangent

Q.

Two circles with centres $ \mathrm{O}$ and $ {\mathrm{O}}^{\text{}}$ of radii $ 3 \mathrm{cm}$ and $ 4 \mathrm{cm}$, respectively intersect at two points $ \mathrm{P}$ and $ \mathrm{Q}$ such that $ \mathrm{OP}$ and $ {\mathrm{O}}^{\text{}}\mathrm{P}$ are tangents to the two circles. Find the length of the common chord $ \mathrm{PQ}$.

Q.

A line segment AB intersects a circle at two distinct points C and D as it passes through its centre, as shown in the figure. The line, whose segment is AB, is a:

1. Tangent

2. Secant

3. Diameter

4. Chord

Q.

If two chords AB and CD intersect externally at P, then PC x PD = _____.

1. PA

2. PA + PB

3. PA - PB

4. PA x PB

Q.

Two circles of radii 5 cm and 3 cm are concentric. Calculate the length of a chord of the outer circle which touches the inner circle.

1. 2 cm

2. 8 cm

3. 23 cm

4. 12 cm

Q. A line segment AB intersects a circle at two distinct points C and D as it passes through its centre, as shown in the figure. The line, whose segment is AB, is:

1. Chord
2. Diameter
3. Secant
4. Tangent

Q. Secant intersects the circle at ___ distinct points.

Q.

A line segment AB intersects a circle at two distinct points C and D as it passes through its centre, as shown in the figure. The line, whose segment is AB, is a:

1. Secant

2. Chord

3. Diameter

4. Tangent

Q.

A line segment AB intersects a circle at two distinct points C and D as it passes through its centre, as shown in the figure. The line, whose segment is AB, is a:

1. Tangent

2. Diameter

3. Chord

4. Secant

Q.

A line that touches a circle at only one point is called ________.

Q. A bicycle wheel has a diameter of 7 cm. What distance does the wheel cover on the ground if it completes 1 full rotation?
(Assume $\pi =\frac{22}{7}$)

1. 44 cm
2. 22 cm
3. 21 cm
4. 42 cm

Q.

A tangent is a secant with which of the following properties?

1. The points of intersection are coinciding points.

2. The secant passes through the centre of the circle.

3. The points of intersection are infinite distance apart.

4. The secant is a curved line.

Q. A tangent is a secant with which of the following properties?

1. The points of intersection are coinciding points.
2. The secant is a curved line.
3. The points of intersection are infinite distance apart.
4. The secant passes through the centre of the circle.

Q.

Two circles touch externally. If their radii measure 10 cm and 8 cm, then the distance between their centres is ____cm.

1. 36

2. 18

3. 16

4. 4

Q.

Two parallel tangents of a circle meet a third tangent at points P and Q. Then, PQ subtends a right angle at the centre.

1. True

2. False

Q.

In the given figure, AB is the diameter of the circle, with centre O, and AT is the tangent calculate the numerical value of x.

1. ${50}^{\circ }$

2. ${58}^{\circ }$

3. ${98}^{\circ }$

4. ${28}^{\circ }$

Q. 𝐀𝐏 is the tangent to the circle with centre 𝐎 and radius 𝟖 𝐜𝐦. If 𝐀𝐁 = 𝟗 𝐜𝐦, then the length of the tangent 𝐀𝐏 is?

Q. There is no tangent to a circle passing through a point lying ..... the circle.

1. inside
2. on the circle
3. outside
4. none of these

Q. In the figure, KLMN is a cyclic quadrilateral and PQ is a tangent to the circle at K. If LN is a diameter of the circle. $\angle KLN={30}^{\circ }$ and $\angle MNL={60}^{\circ }$. Determine $\angle QKN$

1. ${30}^{\circ }$
2. ${100}^{\circ }$
3. ${60}^{\circ }$
4. ${90}^{\circ }$

Q.

A line segment AB intersects a circle at two distinct points C and D as it passes through its centre, as shown in the figure. The line, whose segment is AB, is a:

1. Chord

2. Secant

3. Diameter

4. Tangent

Q. If a secant is drawn to a circle, then under any circumstance, tangents cannot be drawn parallel to the secant.

1. True
2. False

Q.

Two circle touch each externally at point P. Q is a point on the common tangent through P. Then, the tangents QA and QB are equal.

1. True

2. False