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Concentric Circles and a Chord (Posted on 2023-07-19) Difficulty: 3 of 5
Two concentric circles are drawn with chord AB drawn on the larger circle.
AB cuts through the smaller circle at points C and D.
It is known that AC=7, CD=6, and DB=7.

What is the area between the two circles?

For comparison, the classic problem What's the area? is a version where the chord tangent to the inner circle.

See The Solution Submitted by Brian Smith    
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Solution Solution | Comment 2 of 7 |
Draw a perpendicular bisector to AB (passes through the center of the circles).
Connect each of A,B,C,D to the center.
The distance from the center to AB is d
d^2 + 3^2 = r^2
d^2 + 10^2 = R^2
Subtract:  R^2 - r^2 = 10^2 - 3^2 = 91

The area in question is pi*R^2 - pi*r^2
The requested area is 91*pi

  Posted by Larry on 2023-07-19 08:22:25
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