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1965 AMC 12 Question 16

AMC12 · 1965 AMC 12

Question 16

Let line $AC$ be perpendicular to line $CE.$ Connect $A$ to the midpoint $D$ of $CE,$ and connect $E$ to the midpoint $B$ of $AC.$ If $AD$ and $EB$ intersect in point $F,$ and $BC=CD=15$ inches, then the area of triangle $DFE,$ in square inches, is:
  1. $50$
  2. $50\sqrt2$
  3. $75$
  4. $\dfrac{15}{2}\sqrt{105}$
  5. $100$