解题的思维方法常用的有是从条件入手的由因导果法,有从结论入手的由果索因法,还有从两边向中间推进的方法。作为逻辑上的补充,是否存在一种从中间入手,向两边觅求联系的思维方法呢?先看下面几例。 例1 设P为△ABC的重心,AP、BP、CP与△ABC的外接圆交于D、E、F,证明:(数学通报征解第387题) The problem-solving method of thinking is usually based on the principle of directing fruit from the conditions, starting from the conclusion of the law of fruiting, and the method of pushing from the two sides to the middle. As a logical complement, is there a way of thinking that starts from the middle and seeks contact from both sides? Let’s look at the following examples. Example 1 Let P be the center of gravity of △ABC. The circumcircle of AP, BP, CP, and △ABC should be circled at D, E, and F. Prove that: