The length of tangent drawn to a circle of radius 9 cm from a point 41 cm from

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Solution

Q.
The length of tangent drawn to a circle of radius 9 cm from a point 41 cm from the centre is:

1 40 cm

2 9 cm

3 41 cm

4 50 cm

Ans.
(1)

Let O be the centre of the circle and P be the external point and PA is tangent at A as shown in Fig.

$∴ O A ⟂ P A G i v e n, O A = 9 c m a n d O P = 41 c m I n r i g h t Δ O A P, w e h a v e O P^{2} = O A^{2} + P A^{2} (Using Pythagoras theorem) (41)^{2} = (9)^{2} + (P A)^{2} 1681 - 81 = P A^{2} 1600 = P A^{2} \Rightarrow P A = 40 cm$

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