Area of a circle each polygon side is a radius, of length "r". And since the total side length is greater than the circumference, the polygon consists of "n" identical triangles with total area greater than "T". Again we have a contradiction, so our supposition that "C" might be less than "T" must be wrong as well. Therefore, it must be the case that the area enclosed by the circle is precisely the same as the area of the triangle. This concludes the proof. Following Satō Moshun and Leonardo da Vinci , we can use inscribed regular polygons in a different way. Suppose we
Distance from a point to a line The line through these two points is perpendicular to the original line, so Thus, formula_7 and by squaring this equation we obtain: Now consider, using the above squared equation. But we also have, since ("m", "n") is on "ax" + "by" + "c" = 0. Thus, and we obtain the length of the line segment determined by these two points, This proof is valid only if the line is not horizontal or vertical. Drop a perpendicular from the point "P" with coordinates ("x", "y") to the line with equation "Ax" + "By" + "C" = 0. Label the foot of