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The functions of Mathematica package one might want to use to simplify expressions are Simplify and FullSimplify.
Simplify applies simpler algorithms, thus speeding the calculation, and limits the calculation time by 5 minutes.
The use of "assumptions" (refer to Mathematica help) is usually necessary with Simplify and FullSimplify.
At least one should specify that the variables are real. Keep the "assumptions" simple.
In the case of double-object constructions (circle-circle and line-circle crossings) one might confuse the two objects. Plane
always distinguishes such points. The symbolic formula always matches the formula used to calculate the point's coordinates on the screen.
But for some problems one might need to use the first point in one case and the second in another. To correctly match the symbolic expressions one
might need to add an additional "assumption" for Simplify or
FullSimplify. For example, if the first point should be used if a>0 and the second point should be used if a<0, good idea would be
to use formula for first point and add "a>0" in "assumptions" and then to use the formula for the second point with "a<0" in "assumptions".
If ratio for dividing a segment is a variable one may use unique numbers for the ratio and later replace all the occurrences of the numbers in
an expression with symbols.
Use fewer variables and avoid radicals!
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