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Draw a circle of radius 6 cm. From a point 10 cm away from its centre, construct the pair of tangents to the circle and measure their lengths.

Answer :

Steps to construct the required figure:
Step 1: Draw a circle with center O and radius =6cm and draw a point P such that OP=10cm.

Step 2: Draw a perpendicular bisector of OP and mark a point M such that M is the mid- point of OP.

Step 3: With center as M and radius PM=MO, draw a circle which cuts the given circle at S and T.

Step 4: Now join PS and PT.

Thus, we have the required tangents as PS and PT and also the lengths of each tangent is 8cm.


Join OS

Now in the triangle PSO,we have


\(∴ PS= \sqrt{{OP}^2 -{OS}^2} \)
[by pythagoras’ theorem]

\(=\sqrt{{(10)}^2-{(6)}^2}=\sqrt{100-36} \)

\(=\sqrt{64}=8cm \)

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