Assumptions:  the diameter of the Earth and it's shadow are equal,  the line connecting the edges of the illuminated cusps passes the center of the Moon. r^{2} = h (2Rh) R = radius of the Earth r = radius of the Moon r^{2} = 2Rh  h^{2} ≈ 2Rh r/R ≈ 2 h/r Estimate the ratio x=h/r, then the relative radius of the Moon is: r/R ≈2 x 

Result: x ≈ 0.15 r/R ≈ 0.3 Moon: 1737 km, Earth 6371 km r/R=0.273 