python/数学课程/【翻折问题】角平分线2.md

• 延长$AC$至D,使得AD=AB \triangle ABP \cong \triangle ADP

也就是$\triangle APB$根据$AP$翻折后得到\triangle APD

\because \angle APB=150^{\circ} \therefore \angle BPD=60^{\circ} 并且BP=PD $\therefore \triangle PBD$是等边三角形 \because \angle PBC=30^{\circ} \therefore \angle CBD=30^{\circ}

\triangle PBC \cong \triangle BCD,$SAS$ \therefore PC=CD \therefore \angle CPD=\angle CDP 而\angle PDC=\angle ABP=6^{\circ}

\therefore \angle ACP=2*6^{\circ}=12^{\circ}