Question

A circle of radius 3 cm with centre O and a point L outside the circle is drawn, such that OL = 7 cm. From the point L, construct a pair of tangents to the circle. Justify LM and LN are the two tangents.

Answer 1

Steps of construction:

1. Draw a circle with an O in the centre and a radius of 3 cm.
2. Line the outside of the circle with a point so that OL = 7 cm.
3. Make a perpendicular bisector of OL segment. It crosses OL at P.
4. Draw another circle overlapping the given circle at points M and N, with Pas as the centre and radius equal to PL.
5. Join with LM and LN.

Tangents to the circle are segments LM and LN.

Justification: If we join O and M, then

∠OML = 90°  ......[Angle in a semi-circle]

So, LM ⊥ OM

The radius of the circle is shown by OM in the figure.

Therefore, from point L, LM is a tangent to the circle.

Similarly, from point L, LN is a tangent to the circle.