Question 80
Points $A$, $B$, $Y$ and $C$ lie in this order on circle $k$ with center $O$, such that $BC = 2$ cm, $\angle BAY = 42^\circ$ and $\angle CAY = 78^\circ$. It is known that the circle $\omega$ through the points $A$, $O$ and $B$ is tangent to the line $BY$.
The circle through the points $A$ and $C$, tangent to the line $CY$, intersects $\omega$ for the second time at the point $N$. Find:
a) the length of the segment $BO$;
b) the size of the angle $\angle YAN$.
The circle through the points $A$ and $C$, tangent to the line $CY$, intersects $\omega$ for the second time at the point $N$. Find:
a) the length of the segment $BO$;
b) the size of the angle $\angle YAN$.