That is a great point, and in the official exam don't assume r is the radius if not stated....but since we are only allowed to post images and we have to type the question manually it is most likely it was mentioned in the original question that r was the radius of the circle.

In this diagram, the circle is inscribed in a square




ABCD is a square. The circle has a radius r

Quantity A	Quantity B
Length of diagonal AC	\(\frac{5r}{2}\)

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

Solution please...

The diagonal ACV is actually the diameter of the circle. From this we can also conclude that the two side of the square are twice the radius of the circle. As such, 2r

Now we can setup all the necessary to find D

(2r)^2+(2r)^2=d^2

Solve and we do have \(d=\sqrt{8} r\)

Comparing \(\sqrt{8} r\) and \(\frac{5r}{2}\) clearly A > B

A is the answer

suppose, radius of the circle is 5, diameter=side of square=10, diagonal of the square=10root2, which is 10x1.414= 14.14. Quantity B is 5x5/2 which is 12.5, greater than quantity A.

Carcass I believe the answer is wrong here. It should be B

\(\begin{aligned}
(2 r)^2+(2 r)^2 & =d^2 \\
4 r^2+4 r^2 & =d^2 \\
8 r^2 & =d^2 \\
\sqrt{8} r & =d \\
2 \sqrt{2} r & =d
\end{aligned}\)

QA

\(\begin{aligned}
& 2 \sqrt{2} r \\
& 4 \sqrt{2} r \\
& 4 \sqrt{2} \\
& \sqrt{2}
\end{aligned}\)


QB

\(\begin{aligned}
& 5 r \\
& 5 \\
& \frac{5}{4}=1.25
\end{aligned}\)


$\(A B C D\)$ is a square. The circle has radius $\(r\)$. When a circle is inscribed in a square, the diameter of the circle is equal to each side length of the square.

Thank you