# calculated reflected point within circle

The problem to solve is this. Imagine a circle. We know two points on the circumference, anchor A and anchor B, they could be anywhere on the circumference of the circle. Draw a line between these two. Pretend this line is a mirror. Obviously it can be different lengths depending on the anchor points. Then a third point C is added to the circle.
Pretend point C emits a beam of light which always starts its journey travelling horizontally across the circle, so if C is 100 degrees, it takes aim at 260 degrees. The beam encounters the mirror between points A & B. It bounces back at an equal angle from the mirror, what is the angle of the point D where it bounces back and hits the circumference. The size of the circle is immaterial. All we know is the exact angles of A B C around the circle, and that C always travels horizontally; we need a formula to calculate the angle of D on the circumference. Thanks!!

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I think I puzzled out what you meant by 100 degrees and 260, but obviously you don't mean "horizontally". It looks like you mean "diametrically". "From C towards the center" would be a much less convoluted way to say it, too. – rschwieb Sep 12 '12 at 16:46
I think he means that $C = (R \sin 100^o, R \cos 100^o)$ and the ray aims at $(R \sin 260^o, R \cos 260^o)$. In ither words, the ray aims from $C=(x,y)$ at $(-x,y)$, aka. horizontally. – Hagen von Eitzen Sep 12 '12 at 16:47
@hagen Yeah I think you're right. In English, anyhow, "horizontally" cannot be used this way. – rschwieb Sep 12 '12 at 16:53