Bigger, but how big? [Circles I]

Geometry Level 2

There is a minor circle inside a major circle in the diagram below. The minor circle is drawn on a straight line and on the perpendicular of that line, a major circle is drawn with the minor circle's diameter as its radius. Compare the size of the minor circle with the major circle in terms of fractions.

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Exactly 12 37 \frac {12}{37} Approximately 2 7 \frac {2}{7} Approximately 1 4 \frac {1}{4} Exactly 1 4 \frac{1}{4}

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1 solution

Mahdi Raza
May 30, 2020

If radius of smaller circle is r r , the radius of bigger circle will be 2 r 2r . The ratios of area is exactly:

π r 2 4 π r 2 = 1 4 \dfrac{\pi r^2}{4\pi r^2} = \boxed{\dfrac{1}{4}}

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