Tangent, Cotangent, Secant, Cosecant in Terms of Sine and Cosine
In an equilat...
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 ACircumradius is always rational BExradii are always rational CArea is always irrational R = 2r, r=(5−a)tan30∘=53tan30∘⇒s is irrational ⇒Δ is irrational r1=stan30∘=3r (rational)