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MathNet 2019-part-02 — 184 problems (EN–VI) Question 46

Math Olympiad Vault · MathNet 2019-part-02 — 184 problems (EN–VI)

Question 46

In the quadrilateral $ABCD$, we have:
$$
\angle DAB = \angle ABC = \angle BCD = 30^\circ, \quad AB = 4\ \mathrm{cm}, \quad BC = 2\sqrt{3}\ \mathrm{cm}
$$
a) Determine the value of the angle $\angle DCA$.
b) Determine the length of $CD$.
c) Find the area of the quadrilateral $ABCD$.

Question illustration