Using SilverKnight's notation.

sin(<BAF) = BF/BA = (R-1)/(R+1)

cos(<BAF) = FA/BA = 2*√R/(R+1)

sin(<DBC) = DC/DB = 1/(R+1)

sin(<DBC) = sin(2*<BAF) = 2*sin(BAF)*cos(<BAF)

Combining these equations give Brian Smith's cubic.

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