Area of a circle as follows. Draw a perpendicular from the center to the midpoint of a side of the polygon; its length, "h", is less than the circle radius. Also, let each side of the polygon have length "s"; then the sum of the sides, "ns", is less than the circle circumference. The polygon area consists of "n" equal triangles with height "h" and base "s", thus equals ⁄"nhs". But since "h" < "r" and "ns" < "c", the polygon area must be less than the triangle area, ⁄"cr", a contradiction. Therefore, our supposition that "C" might be greater than "T" must be
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