MathDB

The figure shows a triangular pool table with sides

a

b

and

c

. Located at point

S

c

a sphere - which can be assumed as a point. After kick-off, as indicated in the figure, it runs through as a result of reflections to

a, b, a, b

and

c

(in

S

) always the same track. The reflection occurs according to law of reflection. Characterize entilrely all triangles

ABC

, which allow such an orbit, and determine the locus of

S

.
https://cdn.artofproblemsolving.com/attachments/5/b/7662943e5b9ad321226e0c5f5daa3c4ac9faaa.png

Problem Statement