A geometry problem by Matteo Ruth

Geometry Level 4

In \(\triangle ABC \) is \(|AB| = 10, |BC| = 18\) and \( |CA| = 13\). Choose \(A′\) on \([BC]\), \(B′\) on \([AC] \) and \(C′\) on \([AB]\) that the bisectors of \(\triangle ABC\) perpendicular are on the sides of \(\triangle A′B′C'\) like on the picture.

How long is \([A′B]\)?

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