三角形找最短线段，使该线段把三角形分成面积相等的两部分（备忘）

作法：取AC中点M，取AH=AB，取HM中点N，作圆NH，得G，AG即为所求之线段，作圆AG，得D,E，DE即是最短的分割三角形的那根线段。若AB不到AC的一半长，那么DE就是BM，即中线。

用余弦定理即可证明。

几何题：等腰三角形中找点，使内部三个小三角形有相同半径的内切圆

渔夫很幸运地化简了这个等腰的作法， 为任意三角形开了一个好头。看看接下来的运气如何了。

几何题：求三角形内一点使所成的三个三角形有相同半径的内切圆。

这是一个中间产物，却也花了我很多时间，总是发生计算错误的事情，真的不解为何会这样。下一步先看看这个过程是否还有简化的余地，然后继续考虑任意三角形的解法。

不过很高兴终于完成了这个解法。

旁切圆的一些性质

这两天研究了一下旁切圆，发现很有意思，其实很多都没有在教科书上点明白，记在这里备忘。

外心和内心关系图

在做前一个题目时，发现这个关系图。备忘。

a tangent circle in a triangle with one side and the angle(improved)

a very simple solution for this problem.

construction a triangle with bisectors and one side(case1)

construction a triangle with bisectors seems very difficult. Even for Isosceles triangle. This is case I which can be constructed but with the limitation of the bisectors.

construction of a triangle with two side s and inscribe circle

 I have a case which is to construction a triangle with two sides and a inscribe circle.

the case make me confused as it seems a mission impossible. I have plot the graphic of the radius and inner center. but it seems I can only know there is the limitation of the radius and possible two solutions for the construction.

 I had try the simple case which is isosceles triangle but I am also failed for general case. And I got a very interesting and surprising fact is that for the biggest inscribe circle, there is gold ratio point. the angle and tangent point and inner center are all at golden ratio points.

The last picture is the process to construction this triangle with biggest inscribe circle. another interesting fact is also showed in the picture.

I suspect that there is no general compass and straight method to construction for this case.     

sankagu circle 2a

it is the improved version for Sankagu circles. It is better to match the case 1.(more straightforward)

Sankagu circle 2

Sankagu Circle Geo meaning (3 circles)

I am very happy to find a geo method to show the sankagu circle construction .It is nearly perfect!

a tangent circle in a triangle with one side and the angle

this ths part II work of 3 in-circles of a triangle . it seems the problem is tough.

constriction of 2 in-circles in a angel

this is part I work on the question of 3 incircles in a triangle.

sankagu circles 1

this is the simple construction method to construct a sankagu circle which asked by a student.