Find two points across diameter a circle, based on a known position and an isosceles triangle produced from these three points.

Question

I want to find two points across diameter a circle, based on a known position and an isosceles triangle produced from three points that I'll describe as a (the known position) and b and c ( the unknown positions across the diameter of the circle ). This may be pretty basic, so excuse my noobocity.

I think my illustration will describe it better.

point1a, 2a, and 3a positions are known. This center point of the circle is known (here in the center of the 400 x 400 square). The diameter of the circle is known. I want to find position b and c for each a.

Answer 1

Draw a line L from (say) 1a to the center of the circle. Draw a line M through the center of the circle, perpendicular to L. The points where M crosses the circle are your points 1b and 1c.