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In the diagram, point D is the center of the medium-sized circle that passes through C and E, and it is also the center of the largest circle that passes through A and G. Each of the diameters of the small circles with centers B and F equals the radius of the medium-sized circle with center D. The shaded area is what fraction of the largest circle?
Title
Circle with 3 Circles Missing
Your Result
Correct
Difficulty
Hard
Your Pace
0:04
Others' Pace
3:01
Video Explanation
Text Explanation
Let the radius of the smaller circle equal one, so AB = BC = EF = FG = 1. The diameter of one of these smaller circles is 2, so the central medium-sized circle must have a radius of 2, so CD = DE = 2.
Notice that this means that DG = 4, which is the radius of the largest circle. The whole large circle would have an area of
The medium circle has an area of
and each small circle has an area of
If we subtract one medium circle and two smaller circles from the largest circle, we get an area of the shaded region equal to
The ratio of shaded region to whole large circle is
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