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.