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Question

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

A
Circumradius is always rational
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B
Exradii are always rational
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C
Area is always irrational
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D
Perimeter is always rational
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Solution

The correct options are
A Circumradius is always rational
B Exradii are always rational
C Area is always irrational
R = 2r, r=(5a)tan 30=53tan 30 s is irrational Δ is irrational
r1=s tan 30=3r (rational)

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