Construction of Tangent from a Point Outside Circle

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. [3 MARKS]

Q.

Draw a circle of radius 3.5 cm. Construct two tangents from a point 8 cm away from the centre.

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

Q.

The number of direct common tangents to two circles that do not touch or intersect is ____.

1. 4

2. 1

3. 2

4. 3

Q.

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

Q.

Draw a direct common tangent to two congruent circles of radii 3 cm and whose centres are 9 cm apart.

Q. The line joining the centre of a circle and the point from which two tangents are drawn bisects the angle between the tangents. State True or False.

1. False
2. True

Q.

In a circle of radius 4 cm, draw two radii such that the angle between them is 110°. Construct two tangents at the ends of the radii.

Q. Draw a line segment AB of length 7 cm. Taking A as centre, draw a circle of radius 3 cm and taking B as centre, draw another circle of radius 2 cm. Construct tangents to each circle from the centre of the other circle.[4 MARKS]

Q. In Figure 4, a circle is inscribed in a triangle PQR with PQ = 10 cm, QR = 8 cm and PR = 12 cm. Find the lengths QM, RN and PL.

Q. The angle between the tangent and the line joining the point of contact of the tangent to the centre of the circle is ______ .

1. $$0^o$$
2. $${180}^o$$
3. $${360}^o$$
4. $${90}^o$$

Q.

Draw a circle of radius 4 centimetres and draw a regular pentagon with all its sides touching the circle.

Q.

Draw a pair of tangents of radius $2cm$ that are inclined to each other at an angle of $90$ degrees.

Q.

The angle between two tangents to a circle may be $0^{\circ }$.

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.

Construct a tangent to a circle of radius 3 cm at any point ‘P’ on it.

Q.

Construct a transverse common tangent to two circles of radii 2.5 cm and 3 cm with their centres 10 cm apart.

Q. Draw a circle of radius 3.5 cm. Mark s point P outside the circle at a distance of 6 cm from the centre, construct two tangents from P to the given circle. Measure and write down the length of one tangent. [3 MARKS]

Q. Draw a circle of radius 6 cm. Draw a tangent to this circle making an angle of ${30}^{\circ }$ with a line passing through the centre. [3 MARKS]

Q.

Construct a direct common tangent to two circles of radii 5 cm and 3 cm and whose centres are 2 cm apart

Q. Draw a circle of any radius with centre O. Draw two tangents to its inclined at an angle of ${75}^{\circ }$ to each other. [3 MARKS]

Q.

Draw two concentric circles of radii 3 cm and 5 cm. Taking a point on the outer circle, construct the pair of tangents to the inner circle.

Q. To construct a tangent from a point P to a circle (where O is the centre of the circle and P is the point from which tangents are drawn). Following are the steps of construction but they are not in order. Find the correct order of these steps.

(i) Bisect the segment OP, at L.
(ii) Join OP.
(iii) From P, join wherever this circle intersects the original circle.
(iv) Draw a circle with centre as L and radius LO.

1. (ii), (i), (iii), (iv)
2. (i), (ii), (iii), (iv)
3. (i), (ii), (iv), (iii)
4. (ii), (i), (iv), (iiii)

Q.

Construct two circles of radii 2 cm and 3 cm, whose centres are 8 cm apart. Construct a transverse common tangent.

Q.

Draw a circle of radius 3 centimetres and draw a rhombus with one angle 40°, all four sides touching the circle.

Q.

You are given a circle with radius ‘r’ and centre O. You are asked to draw a pair of tangents which are inclined at an angle of ${60}^{\circ }$ with each other. Refer to the figure and select the option which would lead us to the required construction. d is the distance OE.

1. Mark M and N on the circle such that ∠MOE = 60° and ∠NOE = 60°

2. Using trigonometry, arrive at d = r√3 and mark E.

3. Using trigonometry, arrive at d = r√5 and mark E.

4. Construct the ΔMNO as it is equilateral

Q. Construct two tangents to a circle of radius 6 cm from a point 10 cm away from its centre. Write the steps of construction. [3 MARKS]

Q.

Draw a circle of any radius. From a point outside the circle, draw tangents to the circle inclined at 45${}^{\circ }$ to each other. [4 MARKS]

Q.

A pair of tangents can be constructed to a circle inclined at an angle of ${170}^{\circ }$.

1. True

2. False

Q.

Draw a circle of radius 3.5 cm and two perpendicular diameters in it. Construct tangents at the ends of the diameters.