Drawing Tangents to a Circle from a Point on the Circle

Q. Question 2 (iii)
Fill in the blanks:
(iii) A circle can have ___ parallel tangents at the most.

Q.

Construct a tangent to a circle of radius $4cm$ from a point on the concentric circle of radius $6cm$ and measure its length. Also, verify the measurement by actual calculation.

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 it in___ 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 points is___

Q.

In the given figure, PA and PB are two tangents to the circle with center O. If $\angle APB={40}^{\circ }$, find $\angle AQB$ and $\angle AMB$. [4 MARKS]

Q.

In the given figure, AB and AC are tangents to the circle with centre O such that BAC = 40o. Then, BOC is equal to

1. 40^o

2. 150^o

3. 50^o

4. 140^o

Q. Question 4
Draw a pair of tangents to a circle of radius 5 cm which are inclined to each other at an angle of ${60}^{\circ }$.

Q.

Construct a line segment of length 10cm. From one end, draw a circle of radius 4cm and draw a circle of radius 5cm from the other end.
Now, draw tangents to both circles from the centre of the other circle. [4 MARKS]

Q. Draw a circle with centre P. Draw an arc AB of 100° measure. Draw tangents to the circle at point A and point B.

Q.

Draw a circle with centre O and radius 4 cm. Draw any diameter AB of this circle. Construct tangents to the circle at each of the two end points of the diameter AB.

Q.

A circle of radius r has a centre O. What is first step to construct a tangent from a generic point P which is at a distance r from O?

1. With P as centre and radius $>$ r, draw a circle and then join OP.

2. Join OP.

3. With P as centre and radius $<$ r, draw a circle and then join OP.

4. With P as centre and radius = r, draw a circle and then join OP.

Q. Draw any circle. Take any point A on it and construct tangent at A without using the centre of the circle.

Q.

For a tangent, the perpendicular line from the point of contact to the circle passes through the centre.

1. True

2. False

Q.

For a tangent, the perpendicular line from the point of contact to the circle passes through the centre.

1. True

2. False

Q. Take a point O on the plane of a paper. With O as a centre, draw a circle of radius 2.5 cm. Take a point P on this circle, Draw a tangent at P. [3 MARKS]

Q.

Fill in the blanks:

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

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

(iii) A circle can have __________ parallel tangents at the most.

(iv) The common point of a tangent to a circle and the circle is called ____.

Q. Construct a circle of radius 7 cm. Mark a point P on it. Construct a tangent at point P.

Q. Draw a circle of radius 2 cm with centre O and take a point P outside the circle such that OP = 6.5 cm. From P, draw two tangents to the circle.

Q. In the given figure, an isosceles triangle ABC with AB = AC, circumscribes a circle. Prove that the point of contact P bisects the base BC
[CBSE 2012]

Q. Draw a circle of radius 3 cm. Mark a point P at a distance of 5 cm from the centre of the circle. Draw two tangents PA and PB to the given circle and measure the length of each tangent.

Q.

In the given figure, O is the centre of the circle. If PA and PB are tangents from an external point P to the circle, then ∠AQB is equal to

1. 80^o

2. 100^o

3. 50^o

4. 70^o

Q. Divide a line segment of length $10cm$ internally in the ratio $3:2.$

Q. Draw a circle with the help of a bangle. Take a point outside the circle. Construct the pair of tangents from this point to the circle.

Q.

A circle of radius r has a centre O. What is the first step to construct a tangent from a generic point P which is at a distance r from O?

1. With P as centre and radius = r, draw a circle and then join OP.

2. Join OP.

3. With P as centre and radius r, draw a circle and then join OP.

4. With P as centre and radius r, draw a circle and then join OP.

Q. In the figure below, two tangents are drawn from a point P to a circle meeting it at points A and C.
If $\angle AOC={120}^{\circ }$, what is the value of $\angle APC$?

1. ${120}^{\circ }$
2. ${30}^{\circ }$
3. ${80}^{\circ }$
4. ${60}^{\circ }$

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

(a) 30 cm
(b) 28 cm
(c) 25 cm
(d) 31 cm

Q. In the given figure, PA and PB are two tangents drawn from an external point P. If $\angle APB={40}^{\circ }$, then $\angle AOB=$

Q.

In the given figure, PA and PB are two tangents to the circle with center O. If $\angle APB={40}^{\circ }$, find $\angle AQB$ and $\angle AMB$. [4 MARKS]

Q. Construct a tangent to a circle at a given point when the centre of the circle is known.

Q. Question 1
Draw a circle of radius 6 cm. From a point 10 cm away from its centre, construct a pair of tangents to the circle and measure their lengths.

Q.

The point where a tangent meets a circle is called _________.

1. Tangent

2. Point of secant

3. Point of contact

4. End Point of secant