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Geometry Level 3

Let \(\triangle ABC\) rectangle in \(\angle B\) and \(AB<BC\). Take a point \(P\) in bisector of \(\angle ABC\) such that \(AP\) is perpendicular to this bisector. Let \(M\) the middle point of \(AC\), and \(E\) the interseccion of \(MP\) with \(AB\). If \(EM=15\) find \(BC\)

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