>Please note that there are two cases: when right angle
>vertex on chord and when right angle vertex on arc. May be
>there is one simple geometrical proof that the right vertex
>of maximal area triangle must be on arc (as in Peter
>discussion).

Yes, Tuan, the maximal triangle must have the right vertex on the arc. P, the right vertex, has coords (x,y).

Both triangles (right angle on arc(A) or right angle on chord(C)) are valid for all values of x such that 0<x<2.h

For any x in this range areaA>areaC.

Consider xC for which areaC is a maximum. Then areaA is greater.
.: the maximum right triangle has the right angle on arc.

Regards,
Peter Scales
Peter Scales