In the plane rectangular coordinate system, e. f starts from point O, and moves along the positive direction of x-axis at the speed of 1 unit / s, while f moves along the positive direction of y-axis at the speed of 2 units / s, and does not (4,2) make a circle with be as the diameter (1) If e and f start at the same time, let EF and ab compare with G, which is to judge the position relationship between G and circle, and prove that (2) Under the condition of (1), when FB is connected, B is tangent to the circle for a few seconds

In the plane rectangular coordinate system, e. f starts from point O, and moves along the positive direction of x-axis at the speed of 1 unit / s, while f moves along the positive direction of y-axis at the speed of 2 units / s, and does not (4,2) make a circle with be as the diameter (1) If e and f start at the same time, let EF and ab compare with G, which is to judge the position relationship between G and circle, and prove that (2) Under the condition of (1), when FB is connected, B is tangent to the circle for a few seconds

(1) The coordinates of point B are (4,2),
And ∵ OE: of = 1:2, ∵ ofe = ∵ EOB. ∵ FGO = 90?, ∵
And ∵ be is the diameter of ⊙ O1, and ∵ point G is on ⊙ O1
(2) Let B be BM ⊥ of, and OE = X,
Then of = 2x, BF2 = BM2 + FM2 = 42 + (2x-2) 2 = 4x2-8x + 20, be2 = (4-x) 2 + 22 = x2-8x + 20,
And ∵ oe2 + of2 = be2 + BF2, ∵ x2 + 4x2 = 5x2-16x + 40,
That is, BF is tangent to ⊙ O1 in seconds