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MathNet 2008-part-03 — 165 problems (EN–VI) Question 28

Math Olympiad Vault · MathNet 2008-part-03 — 165 problems (EN–VI)

Question 28

In a given rectangle $ABCD$ the length of $AB$ is two times the length of $BC$. On the side $CD$ a point $M$ is chosen such that the angle $AMD$ is equal to the angle $AMB$.

a) Determine the measure of the angle $AMD$.

b) If $\overline{DM} = 1$, determine the area of the rectangle $ABCD$.