Minimum sink
rate occurs at Vmp. Although the drag is more than at
Vmd the fact that it is a lot slower means that your
rate of descent is low.
Maximum range occurs at Vmd where you get the best CL
for the least CD, so that will be at the point of tangency.
On the polar diagram the only points that can be read directly are the top of
the curve, which is CL max or critical alpha, CD min where the graph is furtherest to the left, and the best L/D ratio which is found
at the tangent to the curve from the origin.
You can assume two other points with some accuracy. The best EAS/drag speed
occurs at a speed faster than Vmd so that must be a
smaller angle of attack, or smaller CL so that must be
below the point of tangency to the graph.
Vmp is always slower than Vmd
so must be at a higher angle of attack or CL so it must be between the point of
tangency and CL max.