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 \(BC\).

Source: Disfida Matematica "Urbi et Orbi" (IT)

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