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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.
Solution
Steps of construction:
- Draw a circle with an O in the centre and a radius of 3 cm.
- Line the outside of the circle with a point so that OL = 7 cm.
- Make a perpendicular bisector of OL segment. It crosses OL at P.
- Draw another circle overlapping the given circle at points M and N, with Pas as the centre and radius equal to PL.
- 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.
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