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- - **Rational ratios in triangle**
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Rational ratios in triangleDetermine all triangles ABC such that all of AB/BC,BC/CA,CA/AB,∠A/∠B,∠B/∠C,∠C/∠A are rational |

There are infinite number of such triangles. |

Why? How it can be justified? |

Let edges be a, b, c, and angles be $\displaystyle \alpha , \; \beta , \; \gamma$. $\displaystyle a, \; b, \; c, \; \alpha , \; \beta , \; \gamma \in \mathbb{R}$ and $\displaystyle a/b, \; b/c, \; c/a, \; \alpha / \beta , \; \beta / \gamma , \; \gamma / \alpha \in \mathbb{Q}$ Example is equilateral triangle. It is not easy to solve, hence edges and angles are not necessarily rational. Is there any other hints? |

There is not any hint here... It's really difficult |

tahirimanov is correct for a literal reading of the question, for the reason he stated. But the question remains unanswered for the equivalence class of triangles up to similarity. |

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