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If $b + c : c + a : a + b = 11 : 12 : 13$ then $C o s A : C o s B : C o s C$

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An Intiative by Sri Chaitanya

7:19:25

17:19:5

17:19:25

17:19:15

answer is C.

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Detailed Solution

$b + c : c + a : a + b = 11 : 12 : 13$

$\frac{2 S - a}{11} = \frac{2 S - b}{12} = \frac{2 S - c}{13} = k$

$2 S - a = 11 k$ , $2 S - b = 12 k$

$2 S - c = 13 k$

$a = 7 k, b = 6 k, c = 5 k$

$\cos A : \cos B : \cos C$

$= a (b^{2} + c^{2} - a^{2}) : b (a^{2} + c^{2} - b^{2}) : c (a^{2} + b^{2} - c^{2})$

$= 7 : 19 : 25$

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