# Moving point inside a triangle according to fixed angle

I have a triangle with 3 given points ABC fixed to their X and Y position (must not be changed!). Somewhere inside the triangle is point D , from which three lines go to A B and C. But where exactly is D located?

The only information is the angle between the lines AD, BD and CD.

The angles are:

α between BD and CD: 63.767517418794

γ between AD and CD:160.76124590311

ß between BD and AD:135.47123667809

(I know it should be 360 Degree in total and not 359.99999995, but that is not the point here).

I tried several things to define the size of the angles, but no success. I ended up manually moving it (green numbers, is is only accurate to 3 integers), but I would like to ask whether it is possible to just define 2 of those 3 angles it and D automatically moves at the position.

File name is "triangle with D inside" in my account.

an example:

"But where exactly is D located?"

See appended file.

Construct first the blue triangles, then their circles. At the intersection is D.

Autre construction

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