Question

In the figure above, square $RSTU$ is inscribed in the circle. What is the degree measure of arc $ST$?

• A. ${45}^o$
• B. ${60}^o$
• C. ${90}^o$
• D. ${120}^o$
• E. ${180}^o$

Answer 1

The correct option is C ${90}^o$

Let ${}^{\prime }{O}^{\prime }$ be the center of the given circle.

To find the degree measure of $arc$ $ST$,

We have to find the angle between $\overrightarrow{OS}$ and $\overrightarrow{OT}$.

We have to find the $\angle$$SOT$.

In the square $RSTU$, the diagonals $RT$ and $DS$ subtend an angle of ${90}^0$ between them.

Hence, the angle between $\overrightarrow{OS}$ and $\overrightarrow{OT}$ is ${90}^0$.

$\angle$$SOT$ $=$ ${90}^0$.

Therefore, the degree measure of the $arc$ $ST$ is ${90}^0$.