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Question Number 27959 by ajfour last updated on 17/Jan/18

Commented by ajfour last updated on 17/Jan/18

$$\text{You can't use 'macro parameter character \#' in math mode}$$

Commented by beh.i83417@gmail.com last updated on 17/Jan/18

$$\frac{\mathit{r}}{\mathit{a}/2}=\frac{\mathit{A}x}{xC}\Rightarrow \frac{2r}{a}=\frac{\mathit{A}x}{xC}\Rightarrow \frac{2r+a}{a}=\frac{b}{Cx}$$$$cosC=\frac{a/2}{xC}\Rightarrow xC=\frac{a}{2cosC}$$$$\Rightarrow 2r/a+1=\frac{b}{\frac{a}{2cosC}}=\frac{2bcosC}{a}\Rightarrow$$$$2r+a=2bcosC\Rightarrow r=\frac{1}{2}(2bcosC-a)$$$$1)a^2=b^2+c^2-bc$$$$2)cosC=\frac{a^2+b^2-c^2}{2bc}=\frac{b^2+c^2-bc+b^2-c^2}{2bc}=$$$$=\frac{2b^2-bc}{2bc}$$$$\Rightarrow r=\frac{1}{2}(2b.\frac{2b^2-bc}{2bc}-a)=\frac{2b^2-bc-ac}{2c}$$$$\Rightarrow \mathit{r}=\frac{{\mathit{b}}^2}{\mathit{c}}-\frac{\mathit{a}+\mathit{b}}{2}.◼$$

Commented by ajfour last updated on 17/Jan/18

$$Sir,whatdoesAx,xC,..mean?$$

Commented by beh.i83417@gmail.com last updated on 17/Jan/18

$$x,istheintersectionof\mathit{A}\mathit{C}with$$$$perpendicularlinedrawnfrommidpoint$$$$of\mathit{B}\mathit{C}.$$

Commented by beh.i83417@gmail.com last updated on 18/Jan/18

$$\text{You can't use 'macro parameter character \#' in math mode}$$

Commented by ajfour last updated on 18/Jan/18

$$thankyousir.$$

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