The circumpolygon with maximal area

The convex circumpolygon with maximal area to a given convex polygon can be determined by means of dynamic programming. The effort of this method increases cubically with respect to the number of sides. It is further shown that the optimal circumpolygon can be constructed with ruler and circle. The applied version of dynamic programming can be also used for solving Steiner’s problem of the inpolygon with minimal circumference but it demands a higher effort than Phú’s method.