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2011 AMC 12A Question 24

AMC12 · 2011 AMC 12A

Question 24

Consider all quadrilaterals $ABCD$ such that $AB = 14,$ $BC = 9,$ $CD = 7,$ and $DA = 12.$ What is the radius of the largest possible circle that fits inside or on the boundary of such a quadrilateral?
  1. $\sqrt{15}$
  2. $\sqrt{21}$
  3. $2\sqrt{6}$
  4. $5$
  5. $2\sqrt{7}$