The hypotenuse of a right triangle is 13 cm, and the radius of the inscribed circle is 2 cm. Find the ratio of the area of the circle to the area of the triangle.

["Why Are Right Triangles with a 13 cm Hypotenuse and Inscribed Circle Radius 2 cm Drawing Attention in the US? \nIn a digital world where geometric patterns and math visuals trend across social and search platforms, a lesser-known triangle has quietly gained curiosity. The hypotenuse measuring exactly 13 cm and an inscribed circle radius of 2 cm sparks quiet interest among students, educators, and DIY builders. This specific combination aligns with ancient geometry principles while offering measurable insights into spatial relationships—making it a subtle but meaningful topic in both education and real-world design. As people seek deeper understanding of proportional systems and functional shapes, this precise triangle emerges as a digestible, enlightening puzzle.", "Why This Triangle Is Growing in Conversation \nThe hypotenuse of a right triangle is 13 cm, and the radius of the inscribed circle is 2 cm. This combination isn’t random—it reflects a classic case in right triangle geometry. The inscribed circle’s radius relates directly to the triangle’s inradius formula: \( r = \frac{a + b - c}{2} \), where \( c \) is the hypotenuse. Using \( c = 13 \) and \( r = 2 \), we derive that \( a + b - 13 = 4 \), so \( a + b = 17 \). This constraint tightly limits possible right triangles, making the 13-2 configuration especially instructive. As users explore real-life applications—from architecture to crafting—this ratio of circle to triangle area becomes a small but powerful teaching moment, bridging abstract math and practical use.", "How the Hypotenuse and Inscribed Circle Define the Circle-to-Triangle Area Ratio \nTo find the ratio of the area of the inscribed circle to the area of the right triangle, begin with the circle’s area: \( A_{\ ext{circle}} = \pi r^2 = \pi \cdot 2^2 = 4\pi \). The triangle’s area"]