At the point that corresponds to point C in the model, the skier's line of travel is continued without a kink by a circular arc curve. During travel along this curve, the skier reaches a point that corresponds to point $D ( 18 | - 2 | 2 )$. The circular arc that describes this curve is part of a circle with center $M \left( m _ { 1 } \left| m _ { 2 } \right| m _ { 3 } \right)$. The coordinates of $M$ can be determined using the following system of equations. I $\quad m _ { 1 } + m _ { 2 } + 2 m _ { 3 } - 20 = 0$ II $\quad \left( \begin{array} { l } m _ { 1 } - 9 \\ m _ { 2 } - 1 \\ m _ { 3 } - 5 \end{array} \right) \circ \left( \begin{array} { c } 1.8 \\ 0.2 \\ - 1 \end{array} \right) = 0$ III $\sqrt { \left( m _ { 1 } - 9 \right) ^ { 2 } + \left( m _ { 2 } - 1 \right) ^ { 2 } + \left( m _ { 3 } - 5 \right) ^ { 2 } } = \sqrt { \left( m _ { 1 } - 18 \right) ^ { 2 } + \left( m _ { 2 } + 2 \right) ^ { 2 } + \left( m _ { 3 } - 2 \right) ^ { 2 } }$ Explain the geometric considerations that underlie equations I, II and III.