If one side of an inscribed triangle is a diameter, what can you conclude about the angle opposite that side?

Once you know which angle is $90^\circ$, apply the Pythagorean theorem to find the missing side, then form $\frac{QR}{PR}$ and simplify.

Enter the expression sqrt(130^2-126^2) to compute $QR$.

Enter (sqrt(130^2-126^2))/126 to compute $\frac{QR}{PR}$ as a decimal.

Compute each option as a decimal (for example, enter 16/63, 16/65, etc.) and choose the one that matches the decimal value of $\frac{QR}{PR}$.

The circle has radius 65, so its diameter is $2(65)=130$.

Since $PQ=130$, $PQ$ is a diameter of the circle. An angle that subtends a diameter is a right angle, so $\angle PRQ = 90^\circ$.

In right triangle $PQR$, $PQ$ is the hypotenuse and $PR$ and $QR$ are legs. So:

Substitute $PR=126$ and $PQ=130$:

So $QR=\sqrt{1024}=32$.

So the correct choice is $\frac{16}{63}$.