Draw two tangents to a circle of radius 4 cm from a point P at a distance of 6 cm from its centre.

Steps of construction:

1. Draw a circle of radius 4 cm. Draw a point B, 6cm away from the centre.

2. Join AB. Make perpendicular bisector of AB and let O be the midpoint.

3. Taking O as centre and OA as radius draw a circle.

Let it intersect at C and D. Join BC and BD.

BC and BD are two tangents.

Justification:

We need to prove BC and BD are the tangents to the circle.

Join AC and AD.

As ∠BCA is an angle in the semi-circle of the bigger circle.

Angle in a semi-circle is of 90°.

∠BCA = 90°

∴ AC⊥ BC

Since AC is a radius.

So BC is the tangent as tangent is perependicular to radius.

Similarly BD is tangent.

Hence construction is justifided.