Question #00f2d

1 Answer
Apr 8, 2017

r=sqrt(7/3)r=73

Explanation:

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I assume that AB=BC=CD=1, and DE=EF=FA=2AB=BC=CD=1,andDE=EF=FA=2

As shown in the diagram,
3(x+y)=360^@ => x+y=120^@3(x+y)=360x+y=120
w=(180-x)/2, z=(180-y)/2w=180x2,z=180y2
=> w+z=(360-(x+y))/2=(360-120)/2=120^@w+z=360(x+y)2=3601202=120

In DeltaCDE,
CE^2=CD^2+DE^2-2(CD)(DE)cos(w+z)
CE^2=1^2+2^2-2*1*2*cos120=7

In DeltaOCE,
CE^2=OC^2+OE^2-2(OC)(OE)cos(x+y)
7=r^2+r^2-2r^2cos120
=> 7=2r^2(1-cos120)=2r^2(1-(-1/2))=3r^2
=> r^2=7/3
=> r=sqrt(7/3)