1970 AHSME Problems/Problem 7

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Problem

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 the side of $CD$?

$\text{(A) } \tfrac{1}{2} s(\sqrt{3}+4)\quad \text{(B) } \tfrac{1}{2} s\sqrt{3}\quad \text{(C) } \tfrac{1}{2} s(1+\sqrt{3})\quad \text{(D) } \tfrac{1}{2} s(\sqrt{3}-1)\quad \text{(E) } \tfrac{1}{2} s(2-\sqrt{3})$

Solution

$\fbox{E}$

See also

1970 AHSC (ProblemsAnswer KeyResources)
Preceded by
Problem 6
Followed by
Problem 8
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