# An Algebraic Geometry Problem!

Algebra Level 4

In a $$\Delta ABC$$, let $$a,\ b,\ c$$ be the lengths of the sides of the triangle such that:

• $$b^2=\dfrac{2a^4}{a^4+1}$$
• $$c^2=\dfrac{3b^6}{b^8+b^4+1}$$
• $$a^2=\dfrac{4c^8}{c^{12}+c^8+c^4+1}$$

Find the value of $$\dfrac{a}{b}+\dfrac{b}{c}+\dfrac{c}{a}$$ ?

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