Starting at the lower left, label the four corners of the square as A, B, C, and D. Radius point is E. Intersection of the diagonal line with A-B is F.
From F, a horizontal line intersects C-D at point G. Line FG = 1.
Angle DCE = tan 0.5 = 26.565°
Line CE is the bisector of FCD, thus FCD = 53.130°, leaving CFG as 26.870°.
Cos 26.870 = 0.8000, so line FC = 1/0.8 = 1.25.
My math background is limited compared to some others here, so this presentation is clumsy. IF the answer and reasoning is correct, I'd appreciate a hint or two on how to clean things up.