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MathNet 2008-part-03 — 165 problems (EN–VI) Question 121

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

Question 121

Let $ABCDE$ be a convex pentagon in which $AB=1$, $\angle BAE=\angle ABC=120^\circ$, $\angle CDE=60^\circ$ and $\angle ADB=30^\circ$. Prove that the area of the pentagon $ABCDE$ is less than $\sqrt{3}$.

(Miloš Milosavljević)