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由 tangpakchiu 於 星期日 七月 01, 2007 9:29 pm
#ed_op#DIV#ed_cl#不知對不對...#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#為方便起見,下改Y'為B,X'為A#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#角OXP+角PYO=90度#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#所以O，X，P，Y共圓，角BOP=角XYP#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#角XBY=角XAY=90度，#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#所以X，B，A，Y共圓，角ABY=角AXY#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#要證OP垂直BA，即證角BOP+角OBA=90度#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# 角BOP+角OBA=90度#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#<=>角BOP+角OBA=角OBA+角ABY#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#<=>角BOP=角ABY#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#<=>角XYP=角AXY#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#因XA和PY都垂直PY，#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#所以XA//PY，所以角XYP=角AXY，#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#所以OP垂直BA#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#/DIV#ed_cl#
[數學]幾何題..(87)
由 ☆ ~ 幻 星 ~ ☆ 於 星期日 七月 01, 2007 8:57 pm
已知銳角∠MON內一點P向OM及ON做垂線PX及PY，垂足為X、Y，再從點X、Y分別向ON及OM作垂線XX'和YY'，垂足為X'、Y'
求證：OP垂直X'Y'
求證：OP垂直X'Y'