Circle a triangle whose base has the length of the circle's circumference and whose height equals the circle's radius, which comes to multiplied by the radius squared: Equivalently, denoting diameter by "d", that is, approximately 79% of the circumscribing square (whose side is of length "d"). The circle is the plane curve enclosing the maximum area for a given arc length. This relates the circle to a problem in the calculus of variations, namely the isoperimetric inequality. Equation of a circle<br> In an "x"–"y" Cartesian coordinate system, the circle with centre coordinates ("a", "b") and radius "r" is the set of
Distance from a point to a line formula_19, and formula_20in terms of the coordinates of P and the coefficients of the equation of the line to get the indicated formula. Let "P" be the point with coordinates ("x", "y") and let the given line have equation "ax" + "by" + "c" = 0. Also, let "Q" = ("x", "y") be any point on this line and n the vector ("a", "b") starting at point "Q". The vector n is perpendicular to the line, and the distance "d" from point "P" to the line is equal to the length of the orthogonal projection of formula_21 on n. The