1.
\(\Delta ABC\)中\(E,F\)為\( \overline{AC}\)邊上的三等分點，在\( EB,FB \)上分別有\(G,H\)使得\( \overline{HG}=2\overline{BC} \)，求\( \overline{BF}:\overline{BH} \)的比値？
答案：\( \displaystyle \frac{1}{4} \)
2.
\(x,y\)為實數，求\( \displaystyle \frac{3x+y}{\sqrt{x^2+3y^2}} \)最大值？
答案：\( \displaystyle \frac{2\sqrt{21}}{3} \)
