Matematické Fórum

Skrytý text:

1 :-)
Having two points A,B, than C - to form all accute angles - must lie (better to draw it):
(
Let p call line perpendicular to AB and crossing A
Let q call line perpendicular to AB and crossing B
Let k call circle having AB as diameter
)
1) between p and q
2) ouside k (but this is I think unimportatnt)

The area C can lie is "much smaller" than the rest of the E2 plane where C (forming obtuse angle of ABC triangle) lies. Term "much smaller" can be I think precised by introducing limit of ratio of the areas inscribed into circle with center S (center of AB) and radius x - x is the object of the limit. And the limit is 0 (or infinity - depends on the order denominator - nominator).

But this is only an idea...