Difficult problem

[ins-]

This is an interesting problem in my opinion. I tried to solve it but without considerable success. A former colleague of mine showed it few years ago. He said that the problem may have a practical application - for example for the spherical mirrors on the roads. I like this problem because it is combination between beauty of the math and its practical use.

It is given a circumference k with center O(xo, yo) and radius R, and a segment AB it is defined by the points - A(x1, y1) and B(x2,y2). Find the locus of all the points M lying on k for which the line OM is an angle bisector of the angle AMB.

It is posted on this forum and there was a trial of solution but I can't understand it.

[xaxa3217]

if i correctly read, the locus of all points M will be a line (middle perpendicular at AB) and this is obvious, or my english so bad?:)

[ins-]

Ok ... let say ... I didn't explain it in a good way.
I want to calculate the coordinates of point M in terms of R, x0, y0, x1, y1, x2, y2.