1. The ratio of circumradius and inradius of an equilateral triangle is
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By: anil on 05 May 2019 01.50 am
Circumradius of a triangle = $$R = frac{abc}{4 riangle}$$ Inradius = $$r=frac{2 riangle}{a+b+c}$$ Let the side of the equilateral triangle = $$a$$ cm Also, area of equilateral triangle = $$ riangle = frac{sqrt3}{4}a^2$$ => Ratio of circumradius and inradius = $$(frac{a^3}{4 riangle})div(frac{2 riangle}{3a})$$ = $$frac{3a^4}{8 riangle^2} = frac{3a^4}{8a^4 imes frac{3}{16}}$$ = $$frac{16}{8}=frac{2}{1}$$ => Ans - (C)
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