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ratio wanted, rectangle inscribed in triangle (VII Soros Olympiad R1 9.6)

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July 4, 2021
ratiogeometryrectangle

Problem Statement

Two vertices of the rectangle are located on side BCBC of triangle ABCABC, and the other two are on sides ABAB and ACAC. It is known that the midpoint of the altitude of this triangle, drawn on the side BCBC, lies on one of the diagonals of the rectangle, and the side of the rectangle located on BCBC is three times less than BCBC. In what ratio does the altitude of the triangle divide the side BCBC ?
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