Right triangle inside circle

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

• I don't think you have enough information to do that. I think you need to know $c$ as well... – skyking Nov 1 '17 at 14:04
• Is the $d$ measured along the arc, as you diagram implies? – amd Nov 1 '17 at 19:17
• @amd Yes, "d" is measured along the arc – Vasil Nikolov Nov 2 '17 at 9:08

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 $y_2$.
• @VasilNikolov You're missing the $\sin$. – skyking Nov 1 '17 at 14:49
• It looks to me like $d$ is measured along the arc. – amd Nov 1 '17 at 19:19
• @amd Unfortunately the picture didn't use a large enough $d$ to clearly show the difference. In that case the arc angle would be $d/c$. – skyking Nov 1 '17 at 19:47