I give a very specific example (my problem is more general than that): I have circle C1 and two fixed points (p_a) and (p_b) in C1. C2 and C3 are two circles intersecting with C1. I need to find three points p1 and p2 and p3 s.t: 1. p1 is on C1, p2 on C2 and p3 on C3. 2. p_a, p1 and p2 are on the same line. 3. p_b, p1 and p3 are on the same line. 4. angle (p1, p2, p3) = X 5. angle (p2, p3, p1) = Y Do you think that I can find a deterministic algorithm at least for this specific case ? Thank you.

Yes, square (2) is OK for me. What I really want to do is the following: I have 3 circles as input, and I have to find three points p1, p2 and p3 in these circles (a point in each circle) s.t. the angles of the triangle (p1, p2, p3) satisfy the following: the angle at p1 is equal to a given a1. ... p2 ...a2. ... p3 ...q3. Thank you.

Yes, the meaning is that p1 is on the circle, not in the disk. Thank you for your help.

Find in the sense that there is an exact algorithm that gives the exact points. For example for the intersection of two circles, I can have an algorithm that gives me the exact solution.

@Austin: Thank you, will take a look @Qiaochu: Q2 is mainly to introduce Q3. Geometric predicate, for example, the points p1, ..., pn should a form a regular polygone, or any defined geometric pattern.