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_39 perpendicular to the line. The distance from the point to the line is then just the norm of that vector. This more general formula is not restricted to two dimensions. If the vector space is orthonormal and if the line ("l" ) goes through point A and has a direction vector formula_45, the distance between point P and line ("l") is where formula_47 is the cross product of the vectors formula_48 and formula_45 and where formula_50 is the vector norm of formula_45. Note that cross products only exist in dimensions 3 and 7. Distance from a point to a