# The approach will leave its marks

Geometry Level 4

$\begin{cases} (x_1-x_2)^2+(y_1-y_2)^2=9 \\ (x_2-x_3)^2+(y_2-y_3)^2=16 \\ (x_1-x_3)^2+(y_1-y_3)^2=25 \end{cases}$

If above 3 conditions hold simultaneously,

then find the value of $$\begin{vmatrix} x_1 & y_1 & 1 \\ x_2 & y_2 & 1 \\ x_3 & y_3 & 1 \end{vmatrix}^2$$

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