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A polygon of nine sides, each pf length ...

A polygon of nine sides, each pf length 2, is inscribed in a circle. Prove that the radius of the circle is `cosec 20^(@)`.

Text Solution

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Let AB = 2 units be one of the sides of the polygon.

Then `angleAOB=360^@//9=40^@`, where O is the centre of circle.
If `OL_|_AB," then " AL=1" and " angleAOL=20^@`
`:. " Radius of the circle "=OA=ALcosec20^@=cosec20^@`
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