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AMO 2027 Grades 8-9 SET 25 - Self-study Question 13

AMO · AMO 2027 Grades 8-9 SET 25 - Self-study

Question 13

The diagram shows 28 lattice points, each one unit from its nearest neighbors. Segment $AB$ meets segment $CD$ at $E$. Find the length of segment $AE$.

Question illustration
  1. $\dfrac{4\sqrt5}{3}$
  2. $\dfrac{5\sqrt5}{3}$
  3. $\dfrac{12\sqrt5}{7}$
  4. $2\sqrt5$
  5. $\dfrac{5\sqrt{65}}9$