A 5 cm by 12 cm rectangle is inscribed in a circle. What is the number of centimeters in the circumference of the circle? Express your answer in terms of \(\pi\).

["Title: Find the Circumference of a Circle That Inscribes a 5 cm × 12 cm Rectangle", "When a rectangle is perfectly inscribed in a circle, the circle’s diameter equals the rectangle’s diagonal. For this illustration, we explore what the circumference of such a circle becomes when the rectangle measures 5 cm by 12 cm—an elegant geometry problem perfect for anyone studying circles, rectangles, or circle geometry.", "### Understanding the Geometry", "A circle that perfectly circumscribes a rectangle has the rectangle’s diagonal as the circle’s diameter. To find the circumference, we begin by calculating the length of the diagonal using the Pythagorean theorem.", "Given a rectangle with width 5 cm and height 12 cm, the diagonal (d) is:", "[\nd = \sqrt{5^2 + 12^2} = \sqrt{25 + 144} = \sqrt{169} = 13 \ ext{ cm}\n]", "This diagonal (d = 13) cm is the diameter of the circle.", "### Calculating the Circumference", "The formula for the circumference (C) of a circle is:", "[\nC = \pi \ imes d\n]", "Substituting the diameter:", "[\nC = \pi \ imes 13 = 13\pi \ ext{ cm}\n]", "### Summary", "- The inscribed rectangle (5 cm × 12 cm) produces a diagonal of 13 cm, acting as the circle’s diameter.\n- The circumference is therefore (13\pi) centimeters.", "This cleanly determines the circle’s size in terms of (\pi), a useful outcome in geometry problems involving rectangular symmetry.", "In conclusion: The circumference of the circle in which a 5 cm by 12 cm rectangle is inscribed is exactly (13\pi) centimeters."]