On evolutoids of planar convex curves

There are many interesting curves which we can associate with a given convex curve, however, in this work we are especially interested in studying the relations between the given curve and its evolutoids: that is, the curve obtained as the envelope of lines making a fixed angle with the normal line at every point of the curve. The first result is an inequality between the area enclosed by the given curve and the area enclosed by its evolutoid. Also, we proved that a convex curve is of constant width (centrally symmetric) if and only if its evolutoid for a fixed angle is of constant width (centrally symmetric).