A smaller circle touches a larger circle internally and passes through the center $O$ of the larger circle. If the area of the smaller circle is $200 cm^2$ , what is the area of the larger circle in $cm^2$ ?

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Answer 1 · 2016-11-30T16:37:22

$800$ [ $"cm"^2$ ]

The internal circle tangent to the external and containing the center of external circle, has as diameter the radius of the external.

Calling $r$ radius of internal circle and
$R$ radius of external circle,

$pi r^2=200$ but as already said, $R = 2r$ so
$pi R^2= pi(2r)^2=4pir^2=4 xx 200 = 800$

A smaller circle touches a larger circle internally and passes through the center OO of the larger circle. If the area of the smaller circle is 200 cm^2200 cm^2, what is the area of the larger circle in cm^2cm^2?