## 'Gold Yet Again' printed from http://nrich.maths.org/

In the equilateral triangle inscribed in the circle, $X$ and $Y$ are the midpoints of the edges. Find the ratio${XZ\over XY}$.
The square sits on a diameter of the circle. Find the ratio ${XZ\over XY}$.
The regular pentagon is inscribed in the circle. Find the ratio ${XZ\over XY}$.