Question

Draw a circle of radius 3.0 cm. From a point 7.0 cm away from its centre, construct the pair of tangents to the circle. Write the steps of the construction in brief.

Hint:

To construct tangents from an external point to a circle, use the property that the perpendicular from the centre of the circle to the line joining the external point to the circle bisects the line segment.

Answer 1

Steps of Construction:
1. Draw a circle with a radius of 3.0 cm and centre \( O \).
2. Mark a point \( P \) outside the circle such that the distance \( OP = 7.0 \) cm.
3. Join the centre \( O \) and the point \( P \), and measure the length of \( OP \).
4. From point \( P \), draw a perpendicular bisector to the line \( OP \). This bisector will pass through the point \( Q \), where \( OQ \) is the distance of 3.0 cm (equal to the radius of the circle).
5. Using a compass, draw a circle with centre \( P \) and radius \( PQ \). The two points where this circle intersects the original circle are the points of tangency of the tangents drawn from \( P \) to the circle.
6. From point \( P \), draw straight lines to the two points of intersection. These lines are the required tangents to the circle.
Conclusion:
The pair of tangents from the point \( P \) to the circle are constructed as per the steps mentioned.