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.