# A geometry problem by Filippo Olivetti

Geometry Level 5

Let $$ABC$$ an isosceles triangle with $$BC$$ as base. Let $$r,s$$ be the bisectors of $$\angle BCA$$ and $$\angle CBA$$ rispectivly, and let $$r \cap AB = K$$, $$s \cap AC = R$$. If $$O$$ is the circumcentre of $$ABC$$, then $$R, K, O$$ are allineate. We know that $$OA = 42$$: find the square of the altitude relative to $$BC$$.

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