求救2題資優班考古題
如右圖,在\(\Delta ABC\)中,\(D\)為線段\(\overline{AC}\)上的一點,且\(\overline{BD}\)長為\(\overline{AD}\)長的\(\sqrt{2}\)倍,\(E\)是\(\overline{BD}\)的中點,\(F\)是直線\(EA\)上一點,連接\(\overline{DF}\),並在\(\overline{DF}\)上取一點\(G\),使得\(\angle AGF=\angle CAE\),在直線\(BG\)上取一點\(H\),使得\(\overline{CH}// \overline{AB}\)。
試證:
(1)\(\Delta ABD\)與\(\Delta EAD\)相似。
(2)\(C\)、\(D\)、\(G\)、\(H\)四點共圓。
\(\overline{PA},\overline{PB}\)是圓\(O\)的切線\(\overline{BE}// \overline{PD}\),\(\overline{PD}\)交\(\overline{AE}\)於點\(M\),試證:\(M\)是\(\overline{CD}\)中點。
拜託各位老師了,謝謝