Question Number 62735 by lalitchand last updated on 24/Jun/19
Commented by lalitchand last updated on 24/Jun/19
$$\mathrm{question}\:\mathrm{number}\:\mathrm{26} \\ $$
Answered by mr W last updated on 24/Jun/19
$${area}\:{of}\:{triangle}\:{ABC}=\Delta \\ $$$$\Delta=\frac{{BC}×{AM}}{\mathrm{2}} \\ $$$$\Delta=\frac{{AB}×{OP}}{\mathrm{2}}+\frac{{BC}×{OQ}}{\mathrm{2}}+\frac{{CA}×{OR}}{\mathrm{2}} \\ $$$$\Rightarrow\frac{{AB}×{OP}}{\mathrm{2}}+\frac{{BC}×{OQ}}{\mathrm{2}}+\frac{{CA}×{OR}}{\mathrm{2}}=\frac{{BC}×{AM}}{\mathrm{2}} \\ $$$${AB}={BC}={CA} \\ $$$$\Rightarrow{OP}+{OQ}+{OR}={AM} \\ $$