Right triangle inside circle

Question

I know $a$, $b$, $c$, $x_1$, $y_1$, $\alpha_1$. I want to move the point with distance ($d$) and then calculate $x_2$, $y_2$, $\alpha_2$.

Answer 1

I don't think you have enough information for that, you would need $c$ too (or something to calculate $c$).

The point is that the angle that you rotates the triangle is the difference between $\alpha_2$ and $\alpha_1$. You find that by the fact that $\sin{\alpha_2-\alpha_1\over 2} = {d\over 2c}$. Then you use simple trigonometrics to find $x_2$ and $y_2$.