If an external point of a circle is at a distance equal to the diameter (2r) of the circle from the centre of the circle, then length of the tangent drawn from the external p

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Solution

Q.
If an external point of a circle is at a distance equal to the diameter (2r) of the circle from the centre of the circle, then length of the tangent drawn from the external point is:

1 3r units

2 4r units

3 5r units

4 $\sqrt{3} r u n i t s$

Ans.
(4)

Let P be an external point and O be the centre of the circle, such that OP = 2r units where r is radius of the circle as shown in Fig
Let PA be the tangent at point A on circle.

$∴ O A ⟂ P A a n d O A = r u n i t s N o w, i n r i g h t Δ O A P, w e h a v e A P^{2} + O A^{2} = O P^{2} A P^{2} + r^{2} = (2 r)^{2} A P^{2} = 4 r^{2} - r^{2} = 3 r^{2} A P = \sqrt{3} r units$

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