Concentric Circle Problem

Someone at work showed me this today. I like it!

nice q

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17 thoughts on “Concentric Circle Problem

  1. Pingback: tkz-euclide: Snell’s Law | High School Math and Chess

  2. Pingback: Can You Solve The Ring Area Puzzle? And An Introduction To Visual Calculus – Mind Your Decisions

  3. By varying the arbitrary inner radius an equally varied range of areas can be encompassed by the shaded area.
    A simple exercise with pencil and compass confirms this.
    If the ends of the 10cm line are A & B , its mid point is D and the centre of the circles is C ;
    a generalised formula for the shaded area might read : ( pi times the square of the inner radius CD times the angle ACD over 360) minus 5CD square cm.

  4. If R and r are the larger and smaller circle radii, they form a right triangle with half of the 10 cm line. R^2 = r^2 + 5^2
    So the orange area is (R^2 – r^2) pi which is (5^2) pi or 25 pi cm^2

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