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1983 AMC 12 Question 28

AMC12 · 1983 AMC 12

Question 28

Triangle $ABC$ in the figure has area $10.$ Points $D,$ $E$ and $F,$ all distinct from $A,$ $B$ and $C,$ are on sides $AB,$ $BC$ and $CA$ respectively, and $AD=2,$ $DB=3.$ If triangle $ABE$ and quadrilateral $DBEF$ have equal areas, then that area is

Question illustration
  1. $4$
  2. $5$
  3. $6$
  4. $\frac53\sqrt{10}$
  5. not uniquely determined