The radius of a circle is 8 cm. Calculate the length of a tangent drawn to this circle from a point at a distance of 10 cm from its centre.

6 cm

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8 cm

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10 cm

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16 cm

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Solution

The correct option is A 6 cm

OP = 10 cm, radius OT = 8cm

As PT is tangent to the circle and OT is the radius of the circle, OT is perpendicular to PT.

In triangle OTP,

OT2 + PT2 = OP2

82 + PT2 = 102

PT2 = 100 - 64

PT2 = 36

PT = 6 cm

Therefore option a is correct.

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