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Question Number 98149 by me2love2math last updated on 11/Jun/20

Commented by me2love2math last updated on 11/Jun/20

$$Q1and2pls$$

Answered by mr W last updated on 11/Jun/20

Commented by mr W last updated on 11/Jun/20

$${let}^{\prime }slookattheareaoftriangleABC,$$$$whichis$$$${\mathrm{\Delta }}_{ABC}=\sqrt{s(s-a)(s-b)(s-c)}$$$$withs=\frac{a+b+c}{2}$$$$weseealso$$$${\mathrm{\Delta }}_{ABC}={\mathrm{\Delta }}_{ABO}+{\mathrm{\Delta }}_{ACO}-{\mathrm{\Delta }}_{BCO}$$$$and$$$${\mathrm{\Delta }}_{ABO}=\frac{cr}{2}$$$${\mathrm{\Delta }}_{ACO}=\frac{br}{2}$$$${\mathrm{\Delta }}_{BCO}=\frac{ar}{2}$$$$\Rightarrow {\mathrm{\Delta }}_{ABC}=\frac{(b+c-a)r}{2}=(\frac{a+b+c}{2}-a)r=(s-a)r$$$$\Rightarrow (s-a)r=\sqrt{s(s-a)(s-b)(s-c)}$$$$\Rightarrow r=\sqrt{\frac{s(s-b)(s-c)}{(s-a)}}$$$$$$$$withc=10,b=6,a=7$$$$\Rightarrow s=\frac{10+6+7}{2}=\frac{23}{2}$$$$\Rightarrow r=\sqrt{\frac{\frac{23}{2}(\frac{23}{2}-10)(\frac{23}{2}-6)}{(\frac{23}{2}-7)}}=\frac{\sqrt{759}}{6}\approx 4.59$$

Commented by me2love2math last updated on 12/Jun/20

$$manythx$$

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