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#### Albert

##### Well-known member

- Jan 25, 2013

- 1,225

$\text{if}\,\, \angle A=60^o$

find :

$\dfrac {c}{a+b}+\dfrac {b}{a+c}=?$

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- #1

- Jan 25, 2013

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$\text{if}\,\, \angle A=60^o$

find :

$\dfrac {c}{a+b}+\dfrac {b}{a+c}=?$

Using Cosine formula $\displaystyle \cos (A) = \frac{b^2+c^2-a^2}{2bc}$

Now Given $A = 60^0$ . So $\displaystyle \frac{1}{2} = \frac{b^2+c^2-a^2}{2bc}$

So $b^2+c^2-a^2 = bc \Rightarrow b^2+c^2 = a^2+bc$

Now Given $\displaystyle \frac{c}{a+b}+\frac{b}{a+c} = \frac{c\cdot(a+c)+b\cdot (a+b)}{(a+b)\cdot (a+c)}$

So $\displaystyle = \frac{c^2+ac+b^2+ab}{a^2+ab+bc+ca} = \frac{a^2+ab+bc+ca}{a^2+ab+bc+ca} = 1$

Using $b^2+c^2 = a^2+bc$

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- #3

- Jan 25, 2013

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Can someone find its value using geometry only ?

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- Jan 25, 2013

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