If A(1)A(2)A(3)A(4)A(5) be regular pentg...

If `A_(1)A_(2)A_(3)A_(4)A_(5)` be regular pentgon inscribed in anunit circle. Then `(A_(1)A_(2))(A_(1)A_(3))` is equal to

`sqrt5`

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let A_(1),A_(2),A_(3),...A_(n) are the vertices of a regular n sided polygon inscribed in a circle of radius R.If (A_(1)A_(2))^(2)+(A_(1)A_(3))^(2)+...(A_(1)A_(n))^(2)=14R^(2) then find the number of sides in the polygon.

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Let A_(1), A_(2), A_(3),…,A_(n) be the vertices of an n-sided regular polygon such that (1)/(A_(1)A_(2))=(1)/(A_(1)A_(3))+(1)/(A_(1)A_(4)). Find the value of n. Prove or disprove the converse of this result.

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