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.
I will start by paraphrasing narcoleptic's solution (#4) to the original (tangent) version:
Assume the inner circle has radius 3 (since we don't know it, we can pick one that simplifies the math). The chord cuts through the centers of each circle.
Then the answer is pi*(10^2 - 3^2) = 91*pi.
This depends on the assumption that there is only one answer regardless of the radii of the respective circles.
The generality is verified by:
for d=sym(1):6
a1=atand(sym(3)/d);
r=sym(3)/sind(a1);
a2=atand(sym(10)/d);
R=sym(10)/sind(a2);
area=pi*(R^2-r^2);
disp([d area])
end
for distance of the chord from the center:
[distance, area]
[1, 91*pi]
[2, 91*pi]
[3, 91*pi]
[4, 91*pi]
[5, 91*pi]
[6, 91*pi]
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Posted by Charlie
on 2023-07-19 08:19:47 |
solution
