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Shifted regions (Posted on 2019-02-27) Difficulty: 2 of 5
A circle is centered at the origin with a radius of 5. Two lines are drawn that divide the circle into four regions, the first is the line y=-1, and the other is x=-3. Find the area of the largest region.

No Solution Yet Submitted by Danish Ahmed Khan    
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re: solution - math and computer Comment 4 of 4 |
(In reply to solution - math and computer by Steven Lord)

Going back to my comment, I see I did make a mistake: I used the length of the hypotenuse as the length of one of the legs of one of the right triangles.  But I was not using the right triangles to approximate half sections.

The triangle with that error was the one from (0,0) to (-3,0) to (-3,4), partially filling in what's not covered by the large sector from central angle arcsin(-1/5) to pi/2+arcsin(3/5).

I see my further error now, that I'm thinking about it: the leg of the skinnier triangle at the lower right is also not 5; it's 5*cos(arcsin(1/5)). Now it agrees with your answer, and I have modified my post a second time.

  Posted by Charlie on 2019-02-28 15:33:07
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