# Right-angled triangle

Geometry Level 4

$$\triangle ABC$$ is a right-angled triangle, where $$AC=3$$ and $$BC=4$$. Let $$P$$ be a point on the hypotenuse of the triangle. We drop perpendiculars from $$P$$ to $$AC$$ and $$BC$$, the footpoints of which are $$X$$ and $$Y$$.

If the minimum value of $$\overline{XY}$$ is $$\dfrac{m}{n}$$, where $$m$$ and $$n$$ are coprime integers, then find the value of $$m+n$$.

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