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Three Big Wheels

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How much of the area of a 3 4 5 right triangle can be covered

by three non overlapping circles completely contained by the triangle?

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8 answers to this question

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Posted · Report post

How much of the area of a 3 4 5 right triangle can be covered

by three non overlapping circles completely contained by the triangle?

60%

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Posted · Report post

73.09% if biggest r =1

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74.13% if biggest r =1 medium r = 0.5195 big r = 0.382

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77%

.53 =r1

1.01=r2

.41=r3

looks like i am approaching 80%

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Posted · Report post

I programmed the Malfatti circles for this problem.

They give 66.27% coverage, thought initially to be optimal, clearly not.

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I programmed the Malfatti circles for this problem.

They give 66.27% coverage, thought initially to be optimal, clearly not.

but 1.01 for r1 is stepping on the line..the limit is 1

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Posted · Report post

I programmed the Malfatti circles for this problem.

They give 66.27% coverage, thought initially to be optimal, clearly not.

but 1.01 for r1 is stepping on the line..the limit is 1

The incircle has radius of 1. Good catch ...

The competition is still open.

I'll mark it solved at 74.13 until/unless a better number comes in.

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darn :(

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