Inscribed circle

A circle is inscribed at the bottom wall of the cube with an edge (a = 1). What is the radius of the spherical surface that contains this circle and one of the vertex of the top cube base?

Correct result:

r =  0.8004

Solution:

a=1 r1=a/2=1/2=12=0.5  u=2 a=2 1=21.4142 r2=u/2=1.4142/20.7071  r2=x2+r12 r2=(ax)2+r22  x2+r12=(ax)2+r22 r12=2xa+a2+r22  x=a2+r22r122 a=12+0.707120.522 1=58=0.625  r3=x2+r12=0.6252+0.520.8004  r3=r r=(xa)2+r22=(0.6251)2+0.70712=0.8004



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