Question: A cartographer uses satellite data to map a triangular atoll with side lengths 13 km, 14 km, and 15 km. To optimize GPS signal reception, a circular transmission range must cover the entire triangle. Find the radius of the circumcircle of this triangle, express your answer in simplified radical form.

Sat, 02 May 2026 19:53:32 +0000

**How a Triangular Atoll’s Geometry Powers Perfect GPS Coverage** In a world increasingly defined by precise navigation, understanding how signal coverage works over uneven terrain has become critical—especially for remote atolls where GPS reliability shapes connectivity and safety. A cartographer recently mapped a unique triangular atoll formed by sides measuring 13 km, 14 km, and 15 km—an intriguing case study not just for geography, but for engineering. To ensure every point within this landmass remains receivable by a single circular signal zone, precise geometry determines the minimum radius of the circumcircle. This convergence of mathematics and telecommunications reveals how satellite-enabled GPS systems find optimal coverage for vulnerable coastal environments. With users exploring smarter, more resilient digital infrastructure, this technical marvel offers insight into how physical shape affects digital reach—without a word on the explicit. --- ### Why a Circular Transmission Range Needs the Triangle’s Circumcircle