114學測數學A考科_11

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<多選題>在 \(\triangle ABC\) 中，\(\overline{AB} = 6\)，\(\overline{AC} = 5\)，\(\overline{BC} = 4\)。令 \(\overline{AB}\) 中點為 \(D\)，\(P\) 為 \(\angle ABC\) 之角平分線與 \(\overline{CD}\) 之交點，如右圖所示。試選出正確的選項。
(1) \(\overline{CP} = \frac{3}{7}\overline{CD}\)
(2) \(\overset{\rightharpoonup}{AP} = \frac{3}{7}\overset{\rightharpoonup}{AB} + \frac{2}{7}\overset{\rightharpoonup}{AC}\)
(3) \(\cos \angle BAC = \frac{3}{4}\)
(4) \(\triangle ACP\) 面積為 \(\frac{15}{14}\sqrt{7}\)
(5) (內積) \(\overset{\rightharpoonup}{AP} \cdot \overset{\rightharpoonup}{AC} = \frac{120}{7}\)