MathDB
2015 Geometry #9

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December 23, 2016

Problem Statement

Let ABCDABCD be a regular tetrahedron with side length 11. Let XX be the point in the triangle BCDBCD such that [XBC]=2[XBD]=4[XCD][XBC]=2[XBD]=4[XCD], where [ω‾][\overline{\omega}] denotes the area of figure ω‾\overline{\omega}. Let YY lie on segment AXAX such that 2AY=YX2AY=YX. Let MM be the midpoint of BDBD. Let ZZ be a point on segment AMAM such that the lines YZYZ and BCBC intersect at some point. Find AZZM\frac{AZ}{ZM}.
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