Proof of the Ashi circle
background
Last week's class for junior high school and high school students all talked about Ashi circle, I don't seem to have thought about its proof before, now I have time to try it!
prove
Method 1 Analytical method
Method 2 Cosine Theorem
Method 3 Area method
The above three methods were also thought of after some struggle, and at the beginning it was to prove the special case to find inspiration. The first thing that comes to mind is the analytic method, and then the cosine theorem, so what about Apollonis, the ancient Greeks? He may not have thought of such an advanced method, then he thought that Yuki had a method that junior high school Bonyou could understand, he had been thinking about constructing a similar triangle proof in his mind, and finally combined with the area method learned in the book of Zhang Jingzhong Academician Plane Geometry before, he thought of the third method, so could the vector method be? After the special case is solved, just write down the general situation!
Method FourThe inverse theorem of the angular bisector theorem
After thinking about this, I checked it online, learned other people's ideas, and felt that it was the most beautiful to prove it with the inverse theorem of the angle bisector theorem! Here's how
http://www.360doc.com/content/17/0120/19/37752273_623748447.shtml