sejam ABCD pontos quaisquer, M o ponto médio de AC e N o de BD. exprima x em função de MN, sendo x=AB+AD+CB+CD

\(\[\begin{align} & \text{M=}\frac{\text{(A+C)}}{\text{2}} \\ & \text{Portanto:} \\ & \text{(}\frac{\text{A}}{\text{2}}\text{)+(}\frac{\text{C}}{\text{2}}\text{)} \\ & \text{N=}\frac{\text{(B+D)}}{\text{2}} \\ & \text{(}\frac{\text{B}}{\text{2}}\text{)+(}\frac{\text{D}}{\text{2}}\text{)} \\ & \text{A=2M-C} \\ & \text{B=2N-D} \\ & \text{Logo:} \\ & \text{X=AB+AD+CB+CD} \\ & \text{X=(2M-C)(2N-D)+(2N-C)D+C(2M-D)+CD} \\ & \text{X=4MN-2ND-2MC+CD+2ND-CD+2MC-CD+CD} \\ \end{align}\] \)