#### 12155Question: An isosceles trapezoid with bases $ a $ and $ b $ and legs of length $ c $ is inscribed in a circle. If $ a = 8 $, $ b = 12 $, and $ c = 5 $, what is the radius of the circle?

Mon, 04 May 2026 10:42:55 +0000

# Understanding the Circle Around an Inscribed Isosceles Trapezoid
When a trapezoid with parallel bases of lengths $ a = 8 $ and $ b = 12 $, and equal legs of length $ c = 5 $, is perfectly symmetrical and inscribed within a circle, it reveals a fascinating geometric principle: only certain trapezoids can fit inside a circular shape, and their dimensions determine the circle’s size. This configuration piques interest in geometry enthusiasts, educators, and digital learners exploring spatial relationships and practical applications. Recent trends in STEM education and online geometry exploration highlight growing curiosity about inscribed polygons, especially under real-world conditions. The fact that an isosceles trapezoid achieves this balance—symmetrical sides, equal legs, and perfect circular fit—resonates with current interests in design, architecture, and visual symmetry, encouraging deeper study of mathematical precision. --- ## Why This Is Isn’t Just a Niche Question