延长AO至A'使AO=A'O，延长A'C交MN 于M'，如图：则△OBM≌△OCM'，∴BM=CM'，
∵△NAM∽△NCM'，
∴
| NC |
| AN |
| CM′ |
| AM |
| AC−AN |
| AN |
| AM−AB |
| AM |
∵
| AB |
| AM |
| AC |
| AN |
∴|
| AB| |
| |AM| |
| AC| |
| |AN| |
代入上式得，n-1=1-m，则m+n=2．
| AB |
| AM |
| AC |
| AN |
延长AO至A'使AO=A'O，延长A'C交MN 于M'，如图：| NC |
| AN |
| CM′ |
| AM |
| AC−AN |
| AN |
| AM−AB |
| AM |
| AB |
| AM |
| AC |
| AN |
| AB| |
| |AM| |
| AC| |
| |AN| |