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Junior high school math! The third question is how to do it Don't! Check the original text on a single machine ~ thank you ~
Let me give you a hint. When ∠ ACG = 30, it happens that FG=2, and GA is tangent to circle M.

AF=FG=AG=2

F0= 1

FC=2

CG=FC+GG=2+2=4

F(- 1,0)