In trapezoidal ABCD, AD / / BC, angle bad = 90 °, angle d = 45 °, EF is the middle perpendicular of CD, the perpendicular foot is e, Fe intersects ad at m, if ad = a, calculate BF value

In trapezoidal ABCD, AD / / BC, angle bad = 90 °, angle d = 45 °, EF is the middle perpendicular of CD, the perpendicular foot is e, Fe intersects ad at m, if ad = a, calculate BF value

If CG is perpendicular to ad through C, ABCG is a square, ∠ d = 45, CDG is an isosceles right triangle, CG = GD = AB, ad = Ag + GD = AF + AB = BF