User:Amit6/sandbox20

$$ {AD}^{2}+{BE}^{2}+{CF}^{2}=\frac{2\,{b}^{2}+2\,{c}^{2}-{a}^{2}}{4}+\frac{2\,{a}^{2}+2\,{c}^{2}-{b}^{2}}{4}+\frac{2\,{a}^{2}+2\,{b}^{2}-{c}^{2}}{4} {AD}^{2}+{BE}^{2}+{CF}^{2}=\frac{2\,{b}^{2}+2\,{c}^{2}-{a}^{2}}{4}+\frac{2\,{a}^{2}+2\,{c}^{2}-{b}^{2}}{4}+\frac{2\,{a}^{2}+2\,{b}^{2}-{c}^{2}}{4} {AD}^{2}+{BE}^{2}+{CF}^{2}=\frac{2\,{b}^{2}+2\,{c}^{2}-{a}^{2}}{4}+\frac{2\,{a}^{2}+2\,{c}^{2}-{b}^{2}}{4}+\frac{2\,{a}^{2}+2\,{b}^{2}-{c}^{2}}{4} $$