Incircle and excircles of a triangle polygon with any number of sides that has an inscribed circle—one that is tangent to each side—is called a tangential polygon. Incircle and excircles of a triangle In geometry, the incircle or inscribed circle of a triangle is the largest circle contained in the triangle; it touches (is tangent to) the three sides. The center of the incircle is a triangle center called the triangle's incenter. An excircle or escribed circle of the triangle is a circle lying outside the triangle, tangent to one of its sides and tangent to the extensions of the other two. Every triangle has three
Algebraic geometry points of algebraic geometry. The fact that the field of the real numbers is an ordered field cannot be ignored in such a study. For example, the curve of equation formula_8 is a circle if formula_9, but does not have any real point if formula_10. It follows that real algebraic geometry is not only the study of the real algebraic varieties, but has been generalized to the study of the "semi-algebraic sets", which are the solutions of systems of polynomial equations and polynomial inequalities. For example, a branch of the hyperbola of equation formula_11 is not an algebraic variety, but