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MathNet 2019-part-01 — 184 problems (EN–VI) Question 171

Math Olympiad Vault · MathNet 2019-part-01 — 184 problems (EN–VI)

Question 171

The line $l$ passes through the vertex $D$ of the rectangle $ABCD$ and doesn't have any other common points with this rectangle. The point $M$ lies on $l$, and area of the triangle $MBD$ is twice the area of the triangle $MAD$.
Find all possible values of the ratio of the areas of the triangles $MCD$ and $MAD$.