problem finding a 2D Point in a triangle

I have a Triangle with 3 Points - A, B and C and the angle alpha A and B are fixed. C is any point at the side of 'b' Alpha has at A and B the same size

I need to find any Point on side 'a' except B

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Very confusing: is your triangle isosceles? If C is supposed to be on b, why is there a C in between A and B? Anyway: the knowledge of a point and the angle the line passing though it makes with the horizontal allows you to take points on the line thus determined... –  Ｊ. Ｍ. Jul 17 '11 at 17:17
@J.M. FYI: You should re-upload pictures using ctrl-G because it will then become a permanent imgur image belonging to SE. See Jeff's answer here for some details on that. –  t.b. Jul 17 '11 at 17:18
between A and B is the side 'small c' , point C is the known point above A –  kafioin Jul 17 '11 at 17:20
Thanks @Theo for that. kafioin: A better sketch would be nice, then, where the letters are where they should be... –  Ｊ. Ｍ. Jul 17 '11 at 17:59
I fear I have misunderstood your problem, but if you know the coordinates of both $B$ and $C$, then all the points on the segment $BC=a$ are given by $x B + (1-x) C$, where $x \in [0,1]$. –  Joseph O'Rourke Jul 17 '11 at 18:21