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Relation between Radian and Degree

A sphere of r...

Question

A sphere of radius $a$ ' subtends an angle $60^{0}$ at a point $P$ . Then the distance of $P$ from the center of the sphere is

\frac{a}{\sqrt{3}}

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2 a

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\frac{a \sqrt{3}}{2}

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\frac{2 a}{\sqrt{3}}

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Solution

The correct option is B $2 a$
Consider the given sphere centered at C. Since the angle subtended at P is $60^{0}$ hence the line joining the center of the sphere to P bisects the angle.
$∠ A = ∠ C = 90^{0}$ ...property of tangents.
Therefore consider triangle ACP
$cos 60^{0} = \frac{a}{x}$
$\frac{1}{2} = \frac{a}{x}$
$x = 2 a$
Hence the distance of P from the center of the sphere is 2a.

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A sphere of radius a' subtends an angle 600 at a point P. Then the distance of P from the center of the sphere is

A sphere of radius $a$ ' subtends an angle $60^{0}$ at a point $P$ . Then the distance of $P$ from the center of the sphere is