長方形\(ABCD\)中，\(\overline{AB}=5\)，\(\overline{BC}=4\)。點\(E\)在\(\overline{AB}\)邊上且\(\overline{EB}=1\)，點\(G\) 在\(\overline{BC}\)邊上且\(\overline{CG}=1\)，點\(F\)在\(\overline{CD}\)邊上且\(\overline{DF}=2\)。若線段\(\overline{AG}\) 及\(\overline{AC}\)分別交\(\overline{EF}\)於\(Q\)及\(P\)，則\(\displaystyle \frac{\overline{PQ}}{\overline{EF}}\)之值為何？
(A)\(\displaystyle \frac{\sqrt{3}}{16}\) (B)\(\displaystyle \frac{\sqrt{2}}{13}\) (C)\(\displaystyle \frac{9}{82}\) (D)\(\displaystyle \frac{10}{91}\) (E)\(\displaystyle \frac{1}{9}\)
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114.4.18補充
長方形\(ABCD\)中，\(\overline{AB}=5\)，\(\overline{BC}=6\)。點\(E\)在\(\overline{AB}\)邊上且\(\overline{EB}=2\)，點\(G\)在\(\overline{BC}\)邊上且 \(\overline{CG}=1\)，點\(F\)在\(\overline{AD}\)邊上且\(\overline{AF}=2\)。若線段\(\overline{DE}\)及\(\overline{DB}\)分別交\(\overline{FG}\)於\(P\)及 \(Q\)，則\(\displaystyle \frac{\overline{PQ}}{\overline{FG}}=\)
。
(110嘉義高中資優班，
https://www.cysh.cy.edu.tw/p/403-1008-242-1.php)
