Determine all the triples
![(a, b, c)](/media/m/f/3/a/f3acfeb8e643dcffaff04ac1c181f9af.png)
of positive real numbers such that the system
![a \sqrt{1-x^2}+b \sqrt{1-y^2}-c \sqrt{1-z^2}=0,](/media/m/0/1/e/01e868c3f1bd849c0cad56b1553706ad.png)
is compatible in the set of real numbers, and then find all its real solutions.
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Determine all the triples $(a, b, c)$ of positive real numbers such that the system
$$ax + by -cz = 0,$$ $$a \sqrt{1-x^2}+b \sqrt{1-y^2}-c \sqrt{1-z^2}=0,$$
is compatible in the set of real numbers, and then find all its real solutions.