\(\displaystyle \frac{\Delta BAM}{\Delta BCN}=\frac{\overline{AM}}{\overline{CN}}=\frac{9}{5}\)，\(\displaystyle \frac{\overline{BA}\cdot \overline{BM}}{\overline{BC}\cdot \overline{BN}}=\frac{9}{5}\)
\(\displaystyle \frac{\Delta BAN}{\Delta BCM}=\frac{\overline{AN}}{\overline{CM}}=\frac{20}{16}\)，\(\displaystyle \frac{\overline{BA}\cdot \overline{BN}}{\overline{BC}\cdot \overline{BM}}=\frac{20}{16}\)
\(\displaystyle \frac{\overline{BA}\cdot \overline{BM}}{\overline{BC}\cdot \overline{BN}}\cdot \frac{\overline{BA}\cdot \overline{BN}}{\overline{BC}\cdot \overline{BM}}=\frac{9}{5}\cdot \frac{20}{16}\)
\(\displaystyle \left(\frac{\overline{BA}}{\overline{BC}}\right)^2=\frac{9}{4}\)，\(\displaystyle \frac{\overline{BA}}{\overline{BC}}=\frac{3}{2}\)，\(\displaystyle \frac{\overline{BA}}{15}=\frac{3}{2}\)
\(\displaystyle \overline{AB}=\frac{45}{2}\)
分享解法，共有需要的人參考^^
再次謝謝 thepiano老師 的協助
