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SMO 2019 Junior Round 1 Question 5

SMO · SMO 2019 Junior Round 1

Question 5

In a quadrilateral $ABCD$, the diagonals $AC$ and $BD$ intersect at the point $O$. Suppose that $\angle BAD+\angle ACB=180^\circ$, $|BC|=3$, $|AD|=4$, $|AC|=5$ and $|AB|=6$. What is the value of $\frac{|OD|}{|OB|}$?

Question illustration
  1. $\frac23$
  2. $\frac89$
  3. $\frac9{10}$
  4. $\frac{10}9$
  5. $\frac98$