DOI: https://doi.org/10.36347/sjpms.2026.v13i10.001

Pages: 322-330

This research focuses on finding an exact solution to the problems of “doubling a circle”, "doubling a square" and “doubling a regular triangle”, using only a straightedge and a compass in Euclidean geometry. In 2025, the ancient Greek problem known as "Doubling a Cube" was solved exactly, as documented in https://doi.org/10.14445/22315373/IJMTT-V69I8P506 and https://doi.org/10.36347/sjpms.2025.v12i02.001, [3]. The current problem can be viewed as a derivative issue stemming from the aforementioned Greek challenge. This research aims to determine a circle that possesses double the area of a given circle with area πr², a square that possesses double the area of a given square with area a², and a regular triangle that possesses double the area of a given regular triangle with area A, utilizing only a straightedge and compass within the framework of Euclidean geometry. This research article uses a distinct approach in Geometric Construction to solving the problems.