# 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 '13 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 '13 at 3:38

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.

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Thanks. I think that would work perfectly of course. Now I need to devise a formula for this as I want to apply this to a computer programming problem. –  Mrwolfy Jan 23 '13 at 3:22
That doesn't give tangents! –  vonbrand Jan 23 '13 at 4:01
@vonbrand, who said anything about tangents? OP is looking for two points "across the diameter of the circle," so we are not talking about tangents here (unless OP is very confused about what the problem is). –  Gerry Myerson Jan 23 '13 at 4:07