Strange triangle I

Geometry Level 4

In \(\triangle ABC\) with \(AB=c\), \(AC=b\) and \(BC=a\), where \(\angle A=50^{\circ}\) and \(\angle B=100^{\circ}\), which of the following expressions hold?

\(1. \quad a^3+c^3=3ac^2\\ 2. \quad a^3+c^3=3a^2c\\ 3. \quad 3a^3+c^3=3ac^2\\ 4. \quad 3a^3+c^3=3a^2c\\ 5. \quad 3a^3+b^3=3ab^2\\ 6. \quad 3bc^2+\sqrt{3}c^3=b^3\)

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