###### Advertisements

###### Advertisements

Draw a circle of radius 4 cm. From a point 6 cm away from its centre, construct a pair of tangents to the circle and measure their lengths.

###### Advertisements

#### Solution

**Step of Construction:**Step: I - First of all, we draw a circle of radius AB = 4 cm.

Step: II - Mark a point P from the centre at a distance of 6 cm from the point O.

Step: III - Draw a perpendicular bisector of OP, intersecting OP at Q.

Step: IV - Taking Q as centre and radius OQ = PQ, draw a circle to intersect the given circle at T and T’.

Step: V - Join PT and PT’ to obtain the required tangents.

Thus, PT and PT' are the required tangents.

The length of PT = PT' ≈ 4.5 cm

#### APPEARS IN

#### RELATED QUESTIONS

Draw a line AB = 5 cm. Mark a point C on AB such that AC = 3 cm. Using a ruler and a compass only, construct :

1) A circle of radius 2.5 cm, passing through A and C.

2) Construct two tangents to the circle from the external point B. Measure and record the length of the tangents.

In the figure given below, diameter AB and chord CD of a circle meet at P. PT is a tangent to the circle at T. CD = 7.8 cm, PD = 5 cm, PB = 4 cm. Find:

1) AB.

2) the length of tangent PT.

Using ruler and compasses only construct a triangle ABC in which BC = 4cm, ∠ACB = 45° and perpendicular from A on BC is 2.5 cm. Draw a circle circumscribing the triangle ABC and measure its radius.

Construct an equilateral triangle ABC with side 6 cm. Draw a circle circumscribing the triangle ABC.

Draw a circle circumscribing a regular hexagon with side 5 cm.

Draw a circle of radius 3 cm. Form 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

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

Draw a circle with center 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.

Draw a circle of radius 4.2. Draw a pair of tangents to this circle inclined to each other at an angle of 45°

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

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

Use rule and compass only for answering this question.

Draw a circle of radius 4 cm. Mark the centre as O. Mark a point P outside the circle at a distance of 7 cm from the centre. Construct two tangents to the circle from the external point P.

Measure and write down the length of any one tangent.

Draw two circles of radii 3.5 cm and 2 cm respectively so that their centres are 6 cm apart. Draw direct common tangents to the circle and show that they are equal in length.

Draw two circles of radii 3 cm and 3.5 cm, their centres being 8 cm apart. Construct a transverse common tangent and measure its length.

Draw two circles with radii 2.5 cm and 4 cm and with their centres 7 cm apart.

Draw a direct common tangent and a transverse common tangent. Calculate the length of the direct common tangent.

Draw a circle at a radius of 3 cm. Take a point at 5.5 cm from the center at the circle. From point P, draw two tangents to the circle.

Draw two lines AB, AC so that ∠ BAC = 40°:

(i) Construct the locus of the center of a circle that touches AB and has a radius of 3.5 cm.

(ii) Construct a circle of radius 35 cm, that touches both AB and AC, and whose center lies within the ∠ BAC.

To draw a pair of tangents to a circle which are inclined to each other at an angle of 35°. It is required to draw tangents at the end points of those two radii of the circle, the angle between which is ______.

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

Construct a pair of tangents to a circle of radius 3 cm which are inclined to each other at an angle of 60°.