Construction of Tangents to a Circle from a Point outside the Circle

Q.

Draw a circle of radius 5cm. From any point on the circle, draw a tangent to it. [2 MARKS]

Q. Question 2 (i)
Fill in the blanks:
(i) A tangent to a circle intersects it at ___ point(s).

Q.

Construct two tangents to a circle of radius 4 cm from a point 5 cm. away from the centre.

Q. Draw a circle with centre O and radius 3.5 cm. Take point P at a distance 5.7 cm from the centre. Draw tangents to the circle from point P.

Q. Draw a pair of tangents to a circle of radius 4.5 cm, which are inclined to each other at an angle of 45°. [CBSE 2013]

Q.

Draw 2 concentric circles of radii 3cm and 5cm. Draw tangents to the inner circle from any point on the outer circle. Measure the length of the tangent. [4 MARKS]

Q.

Draw a circle of radius 4 cm. Construct the two tangents to the circle from a P which is at the distance of 7 cm from centre. Measure the length of the tangents

1. 4.7 cm

2. 5.7 cm

3. 7.7 cm

4. 6.7 cm

Q.

Number of tangents from a point lying inside the circle is

1. None

2. Two

3. Infinitely many

4. One

Q. Draw a circle of radius 4 cm. Draw two tangents to the circle inclined at an angle of ${60}^{\circ }$ to each other.

Q.

Draw a circle of radius 3 cm. Extend its diameter and mark two points P and Q each at a distance of 7 cm from the centre. From the points P and Q, draw tangents to the circle and find their approximate lengths.

1. 5.3 cm

2. 5 cm

3. 7 cm

4. 6.3 cm

Q. Draw a circle of radius 3.4 cm and centre E. Take a point F on the circle. Take another point A such that E-F-A and FA = 4.1 cm. Draw tangents to the circle from point A.

Q. Draw a circle of radius 3.6 cm. Draw a tangent to the circle at any point on it without using the centre.

Q. Draw a circle of diameter 6.4 cm. Take a point R at a distance equal to its diameter
from the centre. Measure of tangents from point R is equal to ______ cm (measure approximately)

1. 4.8 cm
2. 5.5 cm
3. 5.7 cm
4. 5.9 cm

Q. The number of tangents that can be drawn from an external point to a circle is [CBSE 2011, 12]
(1) 1
(2) 2
(3) 3
(4) 4

Q.

From which point shown below can we draw one tangent to the following circle?

1. Q

2. Both Q and R

3. Not possible through both Q and R

4. R

Q. Draw a circle of radius 3.5 cm. Take two point A and B on one of its extended diameter, each at a distance of 5 cm from its centre. Draw tangents to the circle from each of these points A and B.

Q. Draw a circle of radius 4 cm. Take a point P on it. Without using the centre of the circle, draw a tangent to the circle at point P. [4 MARKS]

Q. Draw a circle of radius 2.7 cm. Draw a tangent to the circle at any point on it.

Q.

From which point shown below can we draw two tangents to the following circle?

P is a point outside the circle, R inside the circle and Q lies on the circle.

1. P
2. Q
3. R
4. Both P and Q

Q.

Construct a tangent to a circle of radius 5.5 cm from a point 3.5 cm away from it

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.

1. 3 cm

2. 4 cm

3. 5 cm

4. 2 cm

Q.

Construct tangents to a circle of radius 4 cm from a point on the concentric circle of radius 6 cm and find its approximate length.

1. 3 cm

2. 4.5 cm

3. 3.5 cm

4. 4 cm

Q.

Explain the steps to construct tangents to a circle from a point P outside the circle and prove that they are tangents to the circle.

Q.

Question 4
Construct a tangent to a circle of radius 4 cm from a point which is at a distance of 6 cm from its centre of circle.

Q.

Draw a circle of radius $3cm$. From a point$P,7cm$ away from it centre draw two tangents to the circle. Measure the length of each tangent.

Q. Draw a circle of diameter 6.4 cm. Take a point R at a distance equal to its diameter from the centre. Draw tangents from point R.

Q. Construct two tangents to a circle of radius 6 cm from a point 11 cm away from its centre.
[3 marks]

Q.

There is a circle with centre O. P is a point from where only one tangent can be drawn to this circle. What can we say about P?

1. P is inside the circle.

2. P is on the circle.

3. P is outside the circle.

4. None of these

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

Q. Draw a circle of radius 3 cm. From a point P, 7 cm away from the centre of the circle, draw two tangents to the circle. Also, measure the lengths of the tangents. [CBSE 2010]