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1960 AMC 12 Question 38

AMC12 · 1960 AMC 12

Question 38

In this diagram $\overline{AB}$ and $\overline{AC}$ are the equal sides of an isosceles triangle $ABC,$ in which is inscribed equilateral triangle $DEF.$ Designate angle $BFD$ by $a,$ angle $ADE$ by $b,$ and angle $FEC$ by $c.$ Then:

Question illustration
  1. $b=\dfrac{a+c}{2}$
  2. $b=\dfrac{a-c}{2}$
  3. $a=\dfrac{b-c}{2}$
  4. $a=\dfrac{b+c}{2}$
  5. none of these