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Geometry problems in junior high school mathematics entrance examination.
Tan (angle package) = 1/2 It doesn't matter if you don't learn tangent, at least you know: BG/AB= 1/2 (because angle EGF= angle package is 180 -90-angle AGB).

So EF/GF= 1/2. If you haven't learned tangents, use the same scale of similar triangles's sides. ) because EF=CF, GC=CF=EF)

G is the midpoint of BC, so we get BG=GC=CF=EF.

So AB=2BG=CG+CF is AB=GF.

If EF=BG is an equilateral right triangle, the hypotenuse counts. Must be equal.