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Question #00f2d

1 Answer

Apr 8, 2017

#r=sqrt(7/3)#

Explanation:

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

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

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