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1970 AMC 12 Question 7

AMC12 · 1970 AMC 12

Question 7

Inside square $ABCD$ with side $s,$ quarter-circle arcs with radii $s$ and centers at $A$ and $B$ are drawn. These arcs intersect at a point $X$ inside the square. How far is $X$ from side $CD?$
  1. $\tfrac12s(\sqrt3+4)$
  2. $\tfrac12s\sqrt3$
  3. $\tfrac12s(1+\sqrt3)$
  4. $\tfrac12s(\sqrt3-1)$
  5. $\tfrac12s(2-\sqrt3)$