Below is the text description of the problem, please forward it to anyone interested in finding a solution “without using inverse method or trigonometry” while citing the source: In triangle ABC, O is the midpoint of side BC, M and N are on sides AB and AC respectively, AM is equal to AN and angle BOM is equal to angle CON. Prove that AB is equal to AC.
Below is the text description of the problem, please forward it to anyone interested in finding a solution “without using inverse method or trigonometry” while citing the source:
In triangle ABC, O is the midpoint of side BC, M and N are on sides AB and AC respectively, AM is equal to AN and angle BOM is equal to angle CON. Prove that AB is equal to AC.
所以Steiner-Lehmus theorem有正面證法，然後令怡個問題沒有？
將A點視為某圓圓心
若BC線段欲與圓相交於其線段中點，則三角形ABC必等腰
這樣算證畢?
没太看明白
@@zgxk6246BOC結構對稱的狀況下MAN與其相接的方式也必須對稱，否則延長線無法以ABC形成三角
基本上是說角A的角平分線必須通過O點，否則自AM和AN延長至少有一邊碰不到A或B點
只要MAN的角平分線確定通過O點，剩下都是證全等了