Prove the following bcr1 - car2 - abr3 - 2 R - ab - ba - bc - cb - ca - ac - 3 -

L.H.S. = abc [1ar_1 + 1br_2 + 1cr_3] Put r_1 = Ss a and R = abc4S L.H.S. = 4RS. 1S[s aa + s bb + s cc] ...

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Definition of Function

Prove the fol...

Question

Prove the following
$\frac{b c}{r_{1}} + \frac{c a}{r_{2}} + \frac{a b}{r_{3}} = 2 R [(\frac{a}{b} + \frac{b}{a}) + (\frac{b}{c} + \frac{c}{b}) + (\frac{c}{a} + \frac{a}{c}) - 3]$

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\frac{b c}{r_{1}} + \frac{c a}{r_{2}} + \frac{a b}{r_{3}} = 2 R [(\frac{a}{b} + \frac{b}{a}) + (\frac{b}{c} + \frac{c}{b}) + (\frac{c}{a} + \frac{a}{c}) - 3]

∣ ∣ ∣ ∣ ∣ \begin{matrix} b c - a^{2} & c a - b^{2} & a b - c^{2} - b c + c a + a b & b c - c a + a b & b c + c a - a b (a + b) (a + c) & (b + c) (b + a) & (c + a) (c + b) \end{matrix} ∣ ∣ ∣ ∣ ∣ = 3. (b - c) (c - a) (a - b) (a + b + c) (a b + b c + c a)

Δ

A B C

A, B, C

a, b, c

r_{1}, r_{2}

r_{3}

\frac{r_{1}}{b c} + \frac{r_{2}}{c a} + \frac{r_{3}}{a b}

A B C,

(\frac{b - c}{r_{1}}) + (\frac{c - a}{r_{2}}) + (\frac{a - b}{r_{3}}) = 0

(r_{1} - r) / a + (r_{2} - r) / b = c / r_{3}

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