How should the radius MP be drawn?

  • Thread starter Dafoe
  • Start date
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I need help with this one.

http://g.imagehost.org/view/0971/24_p_181 [Broken]


The coloured parts space is limited by three semicircle archs of which the smaller has the radius r.

How should the radius MP be drawn, if you want it to divide the coloured space into two parts with
equally big areas?
 
Last edited by a moderator:

Hurkyl

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What have you tried? Where are you stuck? At first glance, it would look like the most obvious thing would work:

1. Find a convenient way to quantify the position of P
2. Compute a formula for the area of the left blue part
3. Compute a formula for the area of the right blue part
4. Solve for the position of P that makes those areas equal
 

HallsofIvy

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This doesn't require any integration at all. If you draw a vertical downward from M, you cut the blue region into two parts. The area of the left part is 1/4 the area of the large circle plus 1/2 the area of the small circle. What is that?
 

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