# Squares inside a triangle

Geometry Level 5

Given triangle $$ABC$$ with $$BC=115, \sin A=\frac {5}{7}, \frac {AB}{AC}=\frac {3}{5}$$. There is a set of points $$P$$ on segment $$BC$$ satisfying the following:

For each $$P$$ there exists a square $$PQRS$$ such that $$Q,S$$ lie on $$\overline {AC},\overline {AB}$$ respectively, and $$R$$ lies inside triangle $$ABC$$.

Find the length of the segment(s) that these points $$P$$ make up on $$BC$$

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