Circle geometry

All circles are similar, and predictable angle relationships hold inside them: an inscribed angle is always half its matching central angle, and a tangent line is always perpendicular to the radius at the point of tangency. The circumference (2 x pi x r) and area (pi x r^2) formulas can themselves be derived informally by slicing a circle into thin wedges, and the same idea extends to arc length and sector area for just part of a circle; a radian measures an angle by how many radius-lengths its arc spans, so a full circle (circumference 2 x pi x r) is 2 x pi radians. On a coordinate plane, a circle's equation can be found from its radius and center using the Pythagorean theorem, or its center and radius can be found from a given equation by completing the square.

This explanation is AI-generated and can occasionally be wrong. 🚩 Report