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SMO 2006 Senior Round 1 Question 6

SMO · SMO 2006 Senior Round 1

Question 6

In the following figure, $AB$ is the diameter of a circle with centre $O$. It is given that $AB=4$ cm, $BC=3$ cm, and $\angle ABD=\angle DBE$. Suppose the area of quadrilateral $ABCD$ is $x$ cm$^2$ and the area of $\triangle DCE$ is $y$ cm$^2$. Find the ratio $x/y$.

Question illustration
  1. $7$
  2. $8$
  3. $4$
  4. $5$
  5. $6$