In the diagram, the circle is inscribed in the square. This means that the circle and the square share points $S$, $T$, $U$, and $V$, and the width of the square is exactly equal to the diameter of the circle. Rounded to the nearest tenth, what is $XY/XV$, to the nearest tenth?

Answer 1

We see that $\angle XSY$ is a right angle using the radius and tangent at that point. Therefore, line $SY$ contains the diameter of the circle. By symmetry, we get $\angle XVY=\frac{\angle Y}{2}$.
It follows that $\angle XYV=\frac{180-\angle Y}{2}$ so $\angle XVY+\angle XYV=90$ and $\triangle XYV$ is a right triangle. Since $YV$ is a radius of the circle, it is half the length of the square's side and $XY/XV=\boxed{0.7}$.