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

## Trending Questions

**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

**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

4.7 cm

5.7 cm

7.7 cm

6.7 cm

**Q.**

Number of tangents from a point lying inside the circle is

None

Two

Infinitely many

One

**Q.**Draw a circle of radius 4 cm. Draw two tangents to the circle inclined at an angle of 60∘ 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.

5.3 cm

5 cm

7 cm

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)

- 4.8 cm
- 5.5 cm
- 5.7 cm
- 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?

Q

Both Q and R

Not possible through both Q and R

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.

- P
- Q
- R
- 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.

3 cm

4 cm

5 cm

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.

3 cm

4.5 cm

3.5 cm

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 pointP, 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?

P is inside the circle.

P is on the circle.

P is outside the circle.

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∘ [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]