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SMO 2012 Junior Round 1 Question 4

SMO · SMO 2012 Junior Round 1

Question 4

$AB$ is a chord of a circle with centre $O$. The diameter $CD$ is perpendicular to $AB$, with $AB$ closer to $C$ than to $D$. Given $\angle AOB=90^\circ$, find the quotient $[ABC]/[AOD]$.
  1. $\sqrt2-1$
  2. $2-\sqrt2$
  3. $\sqrt2/2$
  4. $(1+\sqrt2)/2$
  5. $1/2$