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AMO 2027 Grades 8-9 SET 9 - Self-study Question 3

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

Question 3

In rectangle $ABCD$, $AD=1$, $P$ is on $AB$, and $DB$ and $DP$ trisect $\angle ADC$. What is the perimeter of $\triangle BDP$?

Question illustration
  1. $3+\frac{\sqrt3}{3}$
  2. $2+\frac{4\sqrt3}{3}$
  3. $2+2\sqrt2$
  4. $\frac{3+3\sqrt5}{2}$
  5. $2+\frac{5\sqrt3}{3}$