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  4. In a Δ Alpha Beta C , if r1=2r2=3r3, , then

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Q. In a $ \Delta \Alpha \Beta C $ , if $ {{r}_{1}}=2{{r}_{2}}=3{{r}_{3}}, $ , then

Bihar CECEBihar CECE 2014

Solution:

Given, $ {{r}_{1}}=2{{r}_{2}}=3{{r}_{3}} $ $ \therefore $ $ \frac{\Delta }{s-a}=\frac{2\Delta }{s-b}=\frac{3\Delta }{s-c} $ $ \Rightarrow $ $ (s-b)=2(s-a) $ and $ (s-c)=3(s-a) $ $ \Rightarrow $ $ \left( \frac{a+b+c}{2}-b \right)=2\left( \frac{a+b+c}{2}-a \right) $ and $ \left( \frac{a+b+c}{2}-c \right)=3\left( \frac{a+b+c}{2}-a \right) $ $ \Rightarrow $ $ a+c-b=2(-a+b+c) $ and $ a+b-c=3(-a+b+c) $ $ \Rightarrow $ $ 3a=3b+c $ and $ 2a=b+2c $ $ \Rightarrow $ $ 4a=5b $ $ \Rightarrow $ $ \frac{a}{b}=\frac{5}{4} $