Question

13£®Ï߶ÎEA£¬AC£¬CB£¬BF×é³ÉÕÛÏßͼÐΣ¬Èô¡ÏC=¦Á£¬¡ÏEAC+¡ÏFBC=¦Â
£¨1£©Èçͼ¢Ù£¬AMÊÇ¡ÏEACµÄƽ·ÖÏߣ¬BNÊÇ¡ÏFBCµÄƽ·ÖÏߣ¬ÈôAM¡ÎBN£¬Ôò¦ÁÓë¦ÂÓкιØϵ£¿²¢ËµÃ÷ÀíÓÉ£®
£¨2£©Èçͼ¢Ú£¬Èô¡ÏEACµÄƽ·ÖÏßËùÔÚÖ±ÏßÓë¡ÏFBCƽ·ÖÏßËùÔÚÖ±Ïß½»ÓÚP£¬ÊÔ̽¾¿¡ÏAPBÓë¦Á¡¢¦ÂµÄ¹ØϵÊǦÁ=¡ÏAPB+$\frac{1}{2}$¦Â»ò¦Á+¡ÏAPB=$\frac{1}{2}$¦Â£®
£¨3£©Èçͼ¢Û£¬Èô¦Á¡Ý¦Â£¬¡ÏEACÓë¡ÏFBCµÄƽ·ÖÏßÏཻÓÚP₁£¬¡ÏEAP₁Óë¡ÏFBP₁µÄƽ·ÖÏß½»ÓÚP₂£»ÒÀ´ËÀàÍÆ£¬Ôò¡ÏP₅=¦Á-$\frac{31}{32}$¦Â£®£¨ÓæÁ¡¢¦Â±íʾ£©

Answer 1

·ÖÎö £¨1£©¸ù¾Ý½Çƽ·ÖÏߵĶ¨Òå±íʾ³ö¡ÏMAC+¡ÏNCB£¬ÔÙ¸ù¾ÝÁ½Ö±ÏßƽÐУ¬ÄÚ´í½ÇÏàµÈ¿ÉµÃ¡ÏC=¡ÏMAC+¡ÏNCB£»
£¨2£©¸ù¾Ý½Çƽ·ÖÏߵĶ¨Òå±íʾ³ö¡ÏPAC+¡ÏPBC£¬ÔÙ·ÖµãPÔÚµãCµÄÏ·½ºÍÉÏ·½Á½ÖÖÇé¿ö£¬ÀûÓÃÈý½ÇÐεÄÒ»¸öÍâ½ÇµÈÓÚÓëËü²»ÏàÁÚµÄÁ½¸öÄڽǵĺÍÁÐʽÕûÀí¼´¿ÉµÃ½â£»
£¨3£©¸ù¾Ý£¨2£©µÄ½áÂÛ·Ö±ð±íʾ³ö¡ÏP₁¡¢¡ÏP₂¡­£¬´Ó¶øµÃ½â£®

½â´ð ½â£º£¨1£©¡ßAMÊÇ¡ÏEACµÄƽ·ÖÏߣ¬BNÊÇ¡ÏFBCµÄƽ·ÖÏߣ¬
¡à¡ÏMAC+¡ÏNCB=$\frac{1}{2}$¡ÏEAC+$\frac{1}{2}$¡ÏFBC=$\frac{1}{2}$¦Â£¬
¡ßAM¡ÎBN£¬
¡à¡ÏC=¡ÏMAC+¡ÏNCB£¬
¼´¦Á=$\frac{1}{2}$¦Â£»

£¨2£©¡ß¡ÏEACµÄƽ·ÖÏßÓë¡ÏFBCƽ·ÖÏßÏཻÓÚP£¬
¡à¡ÏPAC+¡ÏPBC=$\frac{1}{2}$¡ÏEAC+$\frac{1}{2}$¡ÏFBC=$\frac{1}{2}$¦Â£¬
ÈôµãPÔÚµãCµÄÏ·½£¬Ôò¡ÏC=¡ÏAPB+£¨¡ÏPAC+¡ÏPBC£©£¬
¼´¦Á=¡ÏAPB+$\frac{1}{2}$¦Â£¬
ÈôµãPÔÚµãCµÄÉÏ·½£¬Ôò¡ÏC+¡ÏAPB=¡ÏPAC+¡ÏPBC£¬
¼´¦Á+¡ÏAPB=$\frac{1}{2}$¦Â£»
×ÛÉÏËùÊö£¬¦Á=¡ÏAPB+$\frac{1}{2}$¦Â»ò¦Á+¡ÏAPB=$\frac{1}{2}$¦Â£»

£¨3£©ÓÉ£¨2£©µÃ£¬¡ÏP₁=¡ÏC-£¨¡ÏPAC+¡ÏPBC£©=¦Á-$\frac{1}{2}$¦Â£¬
¡ÏP₂=¡ÏP₁-£¨¡ÏP₂AP₁+¡ÏP₂BP₁£©£¬
=¦Á-$\frac{1}{2}$¦Â-$\frac{1}{4}$¦Â=¦Á-$\frac{3}{4}$¦Â£¬
¡ÏP₃=¦Á-$\frac{3}{4}$¦Â-$\frac{1}{8}$¦Â=¦Á-$\frac{7}{8}$¦Â£¬
¡ÏP₄=¦Á-$\frac{7}{8}$¦Â-$\frac{1}{16}$¦Â=¦Á-$\frac{15}{16}$¦Â£¬
¡ÏP₅=¦Á-$\frac{15}{16}$¦Â-$\frac{1}{32}$¦Â=¦Á-$\frac{31}{32}$¦Â£®
¹Ê´ð°¸Îª£º£¨2£©¦Á=¡ÏAPB+$\frac{1}{2}$¦Â»ò¦Á+¡ÏAPB=$\frac{1}{2}$¦Â£»£¨3£©¦Á-$\frac{31}{32}$¦Â£®

µãÆÀ ±¾Ì⿼²éÁËƽÐÐÏßµÄÐÔÖÊ£¬½Çƽ·ÖÏߵĶ¨Ò壬Èý½ÇÐεÄÒ»¸öÍâ½ÇµÈÓÚÓëËü²»ÏàÁÚµÄÁ½¸öÄڽǵĺ͵ÄÐÔÖÊ£¬ÕûÌå˼ÏëµÄÀûÓÃÊǽâÌâµÄ¹Ø¼ü£®