在同一条直线上、故在一条直线上，、在一条直线上，、由西姆松定理可知，、所作垂线的垂足分别为、向若点交于同一点、圆、圆、圆圆也过点同理圆过点，即圆的另一个交点为与圆圆，于点交，于点交中，、线证明：如图，设四条直PNMLPNMNMLPNMLEDACDBCABGGAEDABFCDFBCEGAEDGABFABGFCDABECCGFBGCBGFGCDFBCEFADBCECDABADCDBCAB180?I?A?D?I?A?B?CABCKIO33,330sin120sin30,120,1201801202OHNHMHOHKHKMMHNHMHNHKMCHBKCNBMOHKHOHKHOKHOHKOKHBOCKOHOHOKCOHBOKCOHBOKCHBKOCOBOCHOBHOHCBBHCBOCABHCABOCOKOCOBCHBKBE故又则有：观察又四点共圆。、由垂心的性质由外心的性质、，连结上取解：如图在ABCDPQEFOM?G?I?H?C?A?E?D?B?F?G?I?H?C?A?E?D?B?F?G?F?J?I?H?C?B?O?A?D?L?K?E?F?D?A?B?C?H?J?G?I?H?C?A?E?D?B?F?G?I?H?C?A?E?D?B?F?E?Q?P?O?N?M?K?D?C?B?A
