  We solve several new sharp inequalities relating three quantities amongst the
area, perimeter, inradius, circumradius, diameter, and minimal width of planar
convex bodies. As a consequence, we narrow the missing gaps in each of the
missing planar Blaschke-Santal\'o diagrams. Furthermore, we extend some of
those sharp inequalities into higher dimensions, by replacing either the
perimeter by the mean width or the area by the volume.

Metric Geometry