1. From symmetry, the minimum occurs when OA = OB, where O is the origin. The tangent line (touching the circle at T, say) is then at an angle of 45degrees to the horizontal, and 90 degrees to the radial line OT, so forms 45/45/90 right angled triangles with horizontal and vertical axes. This means TA and TB are the same length as OT, which makes AB = 2
2. Again, symmetry dictates that there is nothing to distinguish a, b, c and d from each other, nor e, f, g and h from each other, so we have :
a4=4e4=9
and (ae)2+(bf)2+(cg)2+(dh)2=4.a2.e2=4.2.3=24