A circle has a chord of length 10, and the distance from the center of the circle to the chord is 5. What is the area of the circle?

$125 \pi$
$100 \pi$
$50 \pi$
$75 \pi$
$25 \pi$

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$A\quad =\quad \pi { r }^{ 2 }\\ A\quad =\quad \pi { (5\sqrt { 2 } ) }^{ 2 }\\ A\quad =\quad 50\pi$