# Now how do I do this?

Geometry Level 4

Let area of the triangle formed by the points $$(b,c)$$, $$(c,a)$$ and $$(a,b)$$ as vertices be $$\Delta$$ and the area of the triangle whose veritces are $$(ac-b^2,ab-c^2)$$, $$(ba-c^2,bc-a^2)$$ and $$(cb-a^2,ca-b^2)$$ be $$\Delta_1$$. Also define $$z$$ as $z = \begin{vmatrix} a&b&c \\ b&c&a \\ c&a&b \end{vmatrix}$ Find the value of $\sqrt{z^2\cdot \dfrac{\Delta}{\Delta_1}}$

Details: Take $$a=3$$, $$b=5$$, $$c=8$$.

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