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.     

Icosikaitrigon construction at 1.2E-11

It is the best solution for Icosikaitrigon construction.It take tow days to simplify the methid which can be finished in normal compass and straight method.

Enneadecagon construction at 1.6E-11

this is the solution for compass and straight to construct a Enneadecagon with least error at 1.6E-11.

construction a Heptagon with error 4E-12

A good news for me. There is a simple method that can construct a Heptagon with relative error at 4E-12,much better than last one. I am afraid that It may not have better solution for simple construction by compass and straight. But I will try further. Let's see what is next.

construction a Heptagon with error 1E-10

I go further to find more accurate method to construction a heptagon. The new method has relative error at 1.14E-10,which is much better than before.The method is not complex so a heptagon can be constructed in a few steps with extremely accuracy.

another simple and accurat classic method to construction the Heptagon

I am happy to find another simple method with relative error 5.7E-9. it is only 6 steps. See the image for the details.

construct heptagon with error at 2.3E-9

It is my pleasure to find a method go beyond 1E-8 for construct Heptagon with classic method. I doubt first if it is possible to use simple method to construct heptagon with relative error less than 1E-8. It seems there is possibility for relative error less than 1E-9. let me try further.

the detail construct steps are on the image.

another simple way to construct Heptagon with hyper accuracy

I found another simple construction method for Heptagon with relative error 4.4E-8.,a tiny better solution than last one. Hope some one will enjoy it.

How to draw a perfect Icosikai-pentagon with compass and straight

Icosikai-pentagon is nonconstructive polygon by compass and straight.

But with the method I post in the picture,one can draw a nearly perfect Icosikai-pentagon with compass and straight.

the first step is to construct a angel which is 9 times of the central angel of the Icosikai-pentagon. the method I found now has little error which make one can use compass and straight drawing perfectly.

it is possible to draw the Icosikai-pentagon with any wanted accuracy. the details post on the previous article.

draw a triskaidecagon with compass and straight

Triskaidecagon(13side polygon) is nonconstructive polygon. I found a simple way to draw it quickly with acceptable error.

the details are on the picture. the idea is to draw a double central angel,since 13 is primer, so you can use this double angel to draw a triskaidecagon quickly.

Be careful to let unit length long enough to make drawing easy.

Anyway ,it is not so perfect and I may
try another way later.