Suppose that the area between a pair of concentric circles is 49pi. Find the length of a chord in the larger circle that is tangent to the smaller circle.

Answer 1

Of we call the two circles r and R, and the center O, draw the tangent and let P be where it touches circle r, and Q be where it intersects R.

Then the triangle OPQ is a right triangle with one leg r and the hypotenuse R. The other leg is thus sqrt(R^2-r^2)

But, pi*R^2 - pi*r^2 = 49pi.
So, R^2-r^2 = 49, and the length of the tangent chord is 14.

Answer 2

Ditto and COPYCAT!

Answer 3

That's true

Answer 4

14

Answer 5

L^2=49.
L=7.
2L=14.
Happy to help- AoPS Hackers

Answer 6

Aops hacker

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Answer 7

Please do not post HW questions here.

Answer 8

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Answer 9

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