Show that b - cr1 - c - ar2 - a - br3 - 0

LHS = #160; (b c)(s a)S + (c a) (s b)S + (a b) (s c)S = #160; sS [b c + c a + a b] #160 ...

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Permutation: n Different Things Taken r at a Time

Show that b...

Question

Show that $\frac{b - c}{r_{1}} + \frac{c - a}{r_{2}} + \frac{a - b}{r_{3}} = 0$

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r_{2}

r_{3}

r_{3}

r_{1}

r_{1}

r_{2}

A B C,

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

△ A B C

a < b < c

r

r_{1}, r_{2}, r_{3}

A, B, C

r < r_{1} < r_{2} < r_{3}

△ A B C, r_{1} r_{2} + r_{2} r_{3} + r_{3} r_{1} = \frac{r_{1} r_{2} r_{3}}{r}

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

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

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