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

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.

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Are the lines from $1a$ to $1b$ and $1c$ tangent to the circle? If so, what makes this different from just each $a$ type point on its own? –  vonbrand Jan 23 at 3:34
actually there is no difference, so maybe I should have had just one example, not three. I was just trying to illustrate that I wanted to calculate these positions dynamically. –  Mrwolfy Jan 23 at 3:38