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Mathematical problems of acacia triangle in the second day of junior high school
S△ABC/S△OB'C=(B'C/BC)2 (similar triangles area ratio is the square of similarity ratio).

So (BC/BC) 2 = 1/2.

Because BC= root number 2

So B'C= 1.

So BB'=(√2- 1)cm.

That is, translation is (√2- 1)cm.