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Question Number 62735 by lalitchand last updated on 24/Jun/19

Commented by lalitchand last updated on 24/Jun/19

question number 26

$$\mathrm{question}\:\mathrm{number}\:\mathrm{26} \\ $$

Answered by mr W last updated on 24/Jun/19

area of triangle ABC=Δ  Δ=((BC×AM)/2)  Δ=((AB×OP)/2)+((BC×OQ)/2)+((CA×OR)/2)  ⇒((AB×OP)/2)+((BC×OQ)/2)+((CA×OR)/2)=((BC×AM)/2)  AB=BC=CA  ⇒OP+OQ+OR=AM

$${area}\:{of}\:{triangle}\:{ABC}=\Delta \\ $$$$\Delta=\frac{{BC}×{AM}}{\mathrm{2}} \\ $$$$\Delta=\frac{{AB}×{OP}}{\mathrm{2}}+\frac{{BC}×{OQ}}{\mathrm{2}}+\frac{{CA}×{OR}}{\mathrm{2}} \\ $$$$\Rightarrow\frac{{AB}×{OP}}{\mathrm{2}}+\frac{{BC}×{OQ}}{\mathrm{2}}+\frac{{CA}×{OR}}{\mathrm{2}}=\frac{{BC}×{AM}}{\mathrm{2}} \\ $$$${AB}={BC}={CA} \\ $$$$\Rightarrow{OP}+{OQ}+{OR}={AM} \\ $$

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