Question 75
The vertices $A,B,C$ of an equilateral triangle of side length $1$ lie on a sphere of radius $1$ and center $O$. Let $D$ be the orthogonal projection of $A$ onto the plane $\alpha$ determined by $B,C,O$. Let $N$ be either intersection of the sphere with the line through $O$ perpendicular to $\alpha$. Find $\angle DNO$.
(Note: the orthogonal projection of $A$ onto $\alpha$ is the intersection of $\alpha$ with the line through $A$ perpendicular to $\alpha$.)
(Note: the orthogonal projection of $A$ onto $\alpha$ is the intersection of $\alpha$ with the line through $A$ perpendicular to $\alpha$.)