If a regular hexagon is inscribed in a circle of radius $r$ , then find the distance between the parallel sides.

\sqrt{3} r

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6 r

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3 r

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12 r

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Solution

The correct option is C $\sqrt{3} r$
In $△ O A C$

$O A = O C = r$

$⟹ ∠ O A C = ∠ O C A$

$∠ O A C = ∠ A O B + ∠ B O C = 60 + 60 = 120$

$2 ∠ O A C = 180 - 120 = 30$

By sine rule

$\frac{A C}{sin 120} = \frac{O C}{sin 30} ⟹ \frac{A C}{\sqrt{3} / 2} = \frac{r}{1 / 2}$

$A C = \sqrt{3} r$

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