(103複賽筆試(二)-臺北市)
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小弟解法為座標化，但碰到一些問題，想請教版友
A擺在座標原點，\(\overline{AB}\)在正x軸
\( \overset{\longleftrightarrow }{AC} \)直線方程: \(2 \sqrt{6}x-5y=0 \)
\(\overset{\longleftrightarrow }{BC} \)直線方程: \( 2 \sqrt{6}x+y-12\sqrt{6}=0 \)
\(\displaystyle \{P \in \{(x,y)| y=mx, 0\leq m \leq \frac{2\sqrt{6}}{5},0 \leq x \leq\frac{12\sqrt{6}}{m+2\sqrt{6}}\} \)
\(d(P, \overline{AB} )=mx \)
\(\displaystyle d(P,\overline{BC})=\frac{12\sqrt{6}-y-2\sqrt{6}x}{5} \)
\(\displaystyle d(P,\overline{AC})=\frac{2\sqrt{6}x-5y}{7} \)
所求=\(\displaystyle \frac{(3m-4\sqrt{6})x+84\sqrt{6}}{35} \) 如何最小化呢?
