In Δ A B C , if a : b : c = 4 : 5 : 6 , then the ratio of the circumradius to its inradius is

Question

In Δ A B C , if a : b : c = 4 : 5 : 6 , then the ratio of the circumradius to its inradius is, 16 : 7, 7 : 16, 4 : 5, 5 : 4

MARKS App · Accepted Answer

We know R = a b c 4 ∆ , r = ∆ s . So R r = a b c 4 ∆ ∆ s = a b c × s 4 ∆ 2 Now a = 4 k , b = 5 k , c = 6 k s = a + b + c 2 = 15 k 2 ⇒ R r = 4 k × 5 k × 6 k × 15 k 4 × 2 × s s - a s - b s - c ⇒ R r = 225 k 4 15 k 2 × 7 k 2 × 5 k 2 × 3 k 2 = 16 7

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