JEE PYQ: Properties Of Triangle Question 8
Question 8 - 2019 (11 Jan Shift 2)
Given $\frac{b + c}{11} = \frac{c + a}{12} = \frac{a + b}{13}$ for a $\triangle ABC$ with usual notation. If $\frac{\cos A}{\alpha} = \frac{\cos B}{\beta} = \frac{\cos C}{\gamma}$, then the ordered triad $(\alpha, \beta, \gamma)$ has a value:
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(1) $(7, 19, 25)$
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(2) $(3, 4, 5)$
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(3) $(5, 12, 13)$
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(4) $(19, 7, 25)$
Show Answer
Answer: (1) $(7, 19, 25)$
Solution
$a = 7k, b = 6k, c = 5k$. Computing: $\cos A = \frac{1}{5}$, $\cos B = \frac{19}{35}$, $\cos C = \frac{5}{7}$. Ratio $= 7 : 19 : 25$.
BETA
