In an equilateral triangle A B C , r : R : r 1 is

Question

In an equilateral triangle A B C , r : R : r 1 is, 1 : 3 : 2, 1 : 3 : 1, 1 : 2 : 3, 2 : 1 : 3

MARKS App · Accepted Answer

In an Equilateral triangle, a = b = c ∴ s = a + b + c 2 = 3 a 2 & ∆ = 3 4 a 2 ∴ r = ∆ s = ∆ 3 a 2 = 2 ∆ 3 a = a 2 3 Also, R = a b c 4 ∆ = a 3 4 3 4 a 2 = a 3 And r 1 = ∆ s - a = ∆ 3 a 2 - a = 2 ∆ a = 3 2 a Now, r : R : r 1 = a 2 3 : a 3 : 3 a 2 = 1 : 2 : 3

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