In an equilateral triangle, if inradius is a rational number then which of the following is /are correct ?

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exradii are alwass rational

circumradius is always rational

perimeter is always rational

area is always ir-rational

answer is A, B, C.

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Detailed Solution

$R = 2 r, r = (s - a) \tan 30^{\circ} = \frac{s}{3} \tan 30^{\circ} \Rightarrow s is irrational \Rightarrow Δ is irrational$
$r_{1} = s \tan 30^{\circ} = 3 r (rational)$

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