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The radius \(r\) of the circle is half the diagonal:
r = \frac{5\sqrt{2}}{2}
C = 2\pi r = 2\pi \left(\frac{5\sqrt{2}}{2}\right) = 5\pi\sqrt{2}
Thus, the circumference of the circle is:
\boxed{5\pi\sqrt{2}}
Given a triangle with sides \(7 \, \text{cm}\), \(24 \, \text{cm}\), and \(25 \, \text{cm}\), find the length of the shortest altitude.
The triangle is a right triangle (since \(7^2 + 24^2 = 25^2\)). The area \(A\) of the triangle is:
A = \frac{1}{2} \times 7 \times 24 = 84 \, \text{cm}^2
The altitude to the hypotenuse \(c = 25\) is:
h_c = \frac{2A}{c} = \frac{168}{25} = 6.72 \, \text{cm}