On the pic.4 we can see the parallelogram in one of the points of the spere.
Sizes of the squares on any of the pictures do not equal to its size on the other pictures but
it does not matter for us. Let's name the left lower angle of the parallelogram by γ. Then:
h
cos β =
------,
sin γ
and γ we can find from this: tg γ is derivative of red ellipse on pic.1 in the point named by M.
Formula of this ellipse is:
x2
y2
------
+
------
= 1,
a2
R2
where R is the radius of the sphere. To find a, substitute co-ordinates of point M on plane for x and y in this formula
(let's name them (xm, ym),
we know them from (1)). So:
xm2
ym2
------
+
------
= 1,
a2
R2
and here is:
xm2R2
a2 =
------------,
R2 - ym2
Assuming that we know a (actually, it is enough to know a2):
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