Math CentralQuandaries & Queries


Question from Conner, a student:

The area of the ring between two concentric circles is 25pi/2 square inches. The length of a chord of the larger circle tangent to the smaller circle is?

Two approaches, one a bit sneaky:

  1. Draw and label a diagram showing the circles, the chord, and the radii to the points where the chord meets the circles. Use Pythagoras' theorem to find the half-chord in terms of the radii. Use the circle-area formula twice to find the area of the ring. Substitute one into the other to solve.

  2. [submit solutions like this at your own risk!] The answer can - it is implied - be found without knowing the radius of the inner circle. So set it to 0. The chord is now a diameter of the outer circle and the problem is easy.

Good Hunting!


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