O 1 and O2 are the center of the unit ball, and the ball O is obviously on MN.
Let OH = R, then: OO 1 = OO2 = R+ 1, thus satisfying the circumscribed condition.
As shown in the figure, establish a spatial coordinate system with m as the origin, and the coordinates of each point are as follows:
O (r，0，r)，？ Oxygen (1, 1, 1)
So: oo2 2 = (1+r) 2
get:( 1-r)2+ 1+( 1-r)2？ = ( 1+r)^2
Solution: r = 3 √ 7
Where r = 3-√ 7 is the solution that meets the meaning of the question.