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Rectangle in a circle (Posted on 2017-11-07) Difficulty: 2 of 5
What is the maximum perimeter
of a rectangle inscribed in
a half of a circle with radius R?

No Solution Yet Submitted by Ady TZIDON    
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Solution Computer solution; not calculus Comment 4 of 4 |
4.472135954999579*R is the Max perimeter
0.8944272*R is the value for x

note:  the downside of this method is there is no easy way to see that the answer is 2*sqrt(5)*R, as noted in the previous solutions.

def y(a):
    """ enter x value and return the y value for a circle of radius 1
    centered at the origin """
    return (1-a**2)**(1/2)

def perim(a):
    """ enter the x value and return the perimeter of a rectangle
    inscribed in a half circle of radius 1 """
    return (4*a + 2*(y(a)))

n = 10000000
x=0
maxPerim = 0
for i in range(1,n):
    newPerim = perim(i/n)
    if newPerim > maxPerim:
        maxPerim=newPerim
        x = i/n

print(x, maxPerim)

  Posted by Larry on 2019-11-18 16:30:22
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