Ray inside a cone.

Hi,

Can anyone provide an elementary solution to this olympiad problem
(ussr I think) :

''A ray of light is issued from a point interior to a given cone. All
the internal surface of this cone can reflect the light.
Prove that after a finite number of reflections, the ray will never
meet the cone again.''

I have seen something dealing with symetrisation with respect to
tangent planes, but I did not understand it...

Thanks in advance,

Pierre.

.

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