Solve {l}{PQ^{2}+QR^{2}=RP^{2}}{PQ^{2}+RP^{2}=QR^2}{RP^2+QR^2=PQ^2}

$$\left. \begin{array} { l } { PQ ^ { 2 } + QR ^ { 2 } = RP ^ { 2 } } \\ { PQ ^ { 2 } + RP ^ { 2 } = QR ^ { 2 } } \\ { RP ^ { 2 } + QR ^ { 2 } = PQ ^ { 2 } } \end{array} \right.$$

Solve for P, Q, R (complex solution)

$$P=0\text{, }Q=0\text{, }R\neq 0$$

$$P=0\text{, }Q\neq 0\text{, }R=0$$

$$P\in \mathrm{C}\text{, }Q=0\text{, }R=0$$

Solve for P, Q, R

$$P=0\text{, }Q=0\text{, }R\neq 0$$

$$P=0\text{, }Q\neq 0\text{, }R=0$$

$$P\in \mathrm{R}\text{, }Q=0\text{, }R=0$$