What is the length of the green line in the following figure?

Question

A hemisphere has a radius of 10.
A cube is constructed so its bottom face has the same center as the hemisphere, and the four corners of its top face just touch the hemisphere.
A green line is constructed from the center of the cube’s top face to a corner of its bottom face, as shown.
What is the length of the green line in the following figure?

Answer 1

10

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See pic below. Green line is equal to red one and red line is equal to radius=10

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Answer 2

First, I calculate the lenght of the cube.
Let´s L= length , R = radius of the hemisphere,
I can write: L exp2 + L/2 exp 2 = R exp 2
Solving this equation, we get L = 8,94
Then ,
Let D= diagonal of the square base,
Dexp 2 = 8,94 exp 2 + 8,94 exp 2 It gives D= 12,64
The final equation is
length of green line exp 2 = 12,64/2 exp 2 + 8,94 exp 2 It gives 10,94
The answer is 10,94