# 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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