In a triangle- if r1-2 r 2-3 r 3- then a - b - b - c - c - a is equal toA- 191-60 155 B- 155-60C- 75-60D- 176-60

The correct option is A Given that, r_1 =2r_2 =3r_3, ∴ nbsp;Δ/s a=2Δ/s b=3Δ/s c=Δ/k (say) Then, s a =k, s b =2k, s c =3k ⇒ 3s (a+b+c)=6k ⇒ nbsp;s=6k ∴ ...

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Standard XII

Mathematics

Ex Radius

In a triangle...

Question

In a triangle, if $r_{1} = 2 r_{2} = 3 r_{3}, t h e n \frac{a}{b} + \frac{b}{c} + \frac{c}{a}$ is equal to

$\frac{75}{60}$

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$\frac{155}{60}$

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$\frac{176}{60}$

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$\frac{191}{60}$

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Solution

The correct option is D
$\frac{191}{60}$

Given that, $r_{1} = 2 r_{2} = 3 r_{3}, ∴ \frac{Δ}{s - a} = \frac{2 Δ}{s - b} = \frac{3 Δ}{s - c} = \frac{Δ}{k} (s a y) T h e n, s - a = k, s - b = 2 k, s - c = 3 k \Rightarrow 3 s - (a + b + c) = 6 k \Rightarrow s = 6 k ∴ \frac{a}{5} = \frac{b}{4} = \frac{c}{3} = k N o w, \frac{a}{b} + \frac{b}{c} + \frac{c}{a} = \frac{5}{4} + \frac{4}{3} + \frac{3}{5} = \frac{75 + 80 + 36}{60} = \frac{191}{60}$

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In a triangle, if r1=2r2=3r3,thenab+bc+ca is equal to

The correct option is D Given that, r1=2r2=3r3,∴Δs−a=2Δs−b=3Δs−c=Δk(say)Then, s−a=k,s−b=2k,s−c=3k⇒3s−(a+b+c)=6k⇒s=6k∴a5=b4=c3=kNow,ab+bc+ca=54+43+35=75+80+3660=19160

In a triangle, if $r_{1} = 2 r_{2} = 3 r_{3}, t h e n \frac{a}{b} + \frac{b}{c} + \frac{c}{a}$ is equal to