Q. 115.0( 3 Votes )
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.
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.
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