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Two circles of radius $~12~$ and $~3~$ touch externally. A line intersecting both of them intersects first circle at points $P$ and $Q$, second circle - at points $R$ and $S$. Three resulting line segments, two inside the circles and the one between them, are equal: $PQ=QR=RS$. Find their common length.

I have prepared a picture with Geogebra to illustrate

I was trying to solve this with no luck.

After formulating it as a system of equations based on coordinates, with the origin being circles' common point and $X$-axis on the line connecting their centers, Wolfram Alpha helped me to find that the answer should be $\frac{3}{2}\sqrt{13}~$.

Can you give any hints on how to solve this?