With usual notation in triangle ABC , the numerical value of ( r 1 + r 2 + r 3 a + b + c ) ( r 1 a + r 2 b + r 3 c ) is

∑ r 1 a = 2 R ∑ 4 R s i n A /2 c o s B /2 c o s C /2 2 s i n A /2 c o s A /2 = ∑ ( tan 2 B + tan 2 C ) = 2 ∑ tan 2 A = 2 ∑ s r 1 = 4 ( a + b + c r 1 + r 2 + r 3 )

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Mathematics - Properties of Triangle Question with Solution | TestHub

MathematicsProperties of Triangler1,r–R formula basedMedium2 minQB

MathematicsMediuminteger

With usual notation in triangle ABC , the numerical value of $(\frac{a + b + c}{r _{1} + r _{2} + r _{3}}) (\frac{a}{r _{1}} + \frac{b}{r _{2}} + \frac{c}{r _{3}})$ is

Answer:

Solution:

$\sum \frac{a}{r _{1}} = 2 R \sum \frac{2 s i n A /2 c o s A /2}{4 R s i n A /2 c o s B /2 c o s C /2} = \sum (tan \frac{B}{2} + tan \frac{C}{2})$

$= 2 \sum tan \frac{A}{2} = 2 \sum \frac{r _{1}}{s} = 4 (\frac{r _{1} + r _{2} + r _{3}}{a + b + c})$

Stream:JEESubject:MathematicsTopic:Properties of TriangleSubtopic:r1,r–R formula based

⏱ 2mℹ️ Source: QB

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