# 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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