Let the tangent $ l$ of the rhombus incircle (I) meet CD, DA at G, H and let (I) touch AB at T. $ \triangle AEH \sim \triangle BEF \sim \triangle CGF$ are similar, having parallel sides. Denote AE = h, EH = a, HA = e sides, s semiperimeter, r the inradius and $ r_a, r_e, r_h$ the A-, E-, H-exradii of $ \triangle AEH.$ (I) is the H-excircle of $ \triangle AEH,$ B-excircle of $ \triangle BEF,$ and G-excircle of $ \triangle CGF.$ Thus ${ \frac {AE}{AT} = \frac {h}{s - e},\ \ \ \frac {CB}{CF} = 1 + \frac {BF}{CF} = 1 + \frac {r_e}{r_{a}}} = 1 + \frac {s - a}{s - e} = \frac {h}{s - e}$ As a result, $ \frac {AE}{AT} = \frac {CB}{CF},$ $ AE \cdot CF = AT \cdot CB.$ But AT, CB are rhombus segments independent of the tangent $ l.$