Given the circle, midpoint $M(0,0)$ and radius $1$, given the points $A(-1,0)$ and $B(1,0)$. Choose $P(\cos \alpha,\sin \alpha)$. The line $MS\ :\ y=\frac{\sin \alpha-\cos \frac{\alpha}{2}}{\cos \alpha+\sin \frac{\alpha}{2}} \cdot x$ intersects the line $PB\ :\ y=-\frac{\cos \frac{\alpha}{2}}{\sin \frac{\alpha}{2}}(x-1)$ in the point $S(\sin \frac{\alpha}{2}+\cos \alpha,\sin \alpha-\cos \frac{\alpha}{2})$. $\triangle PMS\ :\ PM=1,PS^{2}=\sin^{2}\frac{\alpha}{2}+\cos^{2}\frac{\alpha}{2}=1,MS^{2}=2-2\sin \frac{\alpha}{2}$.