Raio da Circunferência Circunscrita

The circumscribed circle radius calculator determines the radius of the circle that passes through the three vertices of a triangle. It uses the formula R = abc/(4A), where a, b, and c are the side lengths and A is the area. The result is useful in geometry, engineering, and design problems involving triangles inscribed in circles.

Simply input the three side lengths and the area. The calculator applies the formula directly, providing the circumradius. Ensure consistent units (e.g., centimeters for sides and square centimeters for area) for an accurate result. The formula derives from the law of sines and works for any triangle, as long as the area is known.

Use this calculator in scenarios like designing gears, calculating dimensions of triangular mechanical parts, solving school or college geometry problems, or in architecture to determine the circle circumscribing a triangular structure. It is especially helpful when you know the sides and area but not the circumradius.

Caution: verify that the entered area is positive and corresponds to the triangle with the given sides. The formula assumes a non-degenerate triangle (positive sides satisfying the triangle inequality). For right triangles, the circumradius equals half the hypotenuse, which can serve as a quick check.