\[ \large \frac{AN}{BN} \cdot \frac{BL}{CL} \cdot \frac{CM}{AM} = 1 \]
證明
透過正弦定理，有\[\frac{AN}{AM} = \frac{\sin\beta}{\sin\alpha} \] 同理可得，\[\frac{BL}{BN} = \frac{\sin\alpha}{\sin\gamma} , \frac{CM}{CL} = \frac{\sin\gamma}{\sin\beta} \] 相乘即可得 \[\frac{AN}{AL} \cdot \frac{BL}{BN} \cdot \frac{CM}{CL} = \frac{\sin\beta}{\sin\alpha} \cdot \frac{\sin\alpha}{\sin\gamma} \cdot \frac{\sin\gamma}{\sin\beta} = 1 \]
參考資料: Wikipedia
