Hello, below is some maple code for a plot of two curves. I need to figure out how to find the common tangent line between these two curves. Thanks!

\( \begin{array}{l}G a \text { alpha }:=20000 \\ \text { Ga_bela }:=-2000 \\ G a_{-} \text {beta }:=-2000 \\ G b \text { bela: }=-25000 \\ \text { Gb bela := }-25000 \\ \text { Gh_alpha }:=-3000 \text {; } \\ \text { (ab alpha :=-3000 } \\ \text { 10_alpha:= }-15000 \text {; } \\ \text { 10_alpha:= }-15000 \\ \text { Lo_beta:= }-17000 \\ \text { LO_beta:= }-17000 \\ \text { LI_alpha:= - 12000; } \\ \text { LI_alpha }:=-12000 \\ \text { I.]_beta:=0; } \\ \text { I.I_beta }:=0 \\ x A:=(1-x B) \\ x A:=1-x B \\ R:=8.314 \\ R:=8.314 \\ G a:=x A \cdot(\text { Ga_alpha })+x B \cdot\left(G b \_a l p h a ight) \cdot x B+R \cdot T \cdot(x A \cdot \ln (x A)+x B \cdot \ln (x B))+x A \cdot x B \\ \left.\text { - } \text { Lo_alpha }+(x A-x B) \cdot I I \_a l p h a ight) \\ a:=-20000+20000 x B-3000 x B^{2}+7482.600 x B \ln (x B)+7482.600(1-x B) \ln (1-x B) \\ +(1-x B) x B(-27000+24000 x B) \\ G b:=x A \cdot(G a \text { beta })+x B \cdot(G b \text { beta }) \cdot x B+R \cdot T \cdot(x A \cdot \ln (x A)+x B \cdot \ln (x B))+x A \cdot x B \\ \text { - }(L 0 \text { beia }+(x A-x B) \cdot L 1 \text { beta }) \\ f b:=-2000+2000 x B-25000 x B^{2}+7482.600 x B \ln (x B)+7482.600(1-x B) \ln (1-x B) \\\end{array} \) \( \begin{array}{l}G a \text { alpha }:=20000 \\ \text { Ga_bela }:=-2000 \\ G a_{-} \text {beta }:=-2000 \\ G b \text { bela: }=-25000 \\ \text { Gb bela := }-25000 \\ \text { Gh_alpha }:=-3000 \text {; } \\ \text { (ab alpha :=-3000 } \\ \text { 10_alpha:= }-15000 \text {; } \\ \text { 10_alpha:= }-15000 \\ \text { Lo_beta:= }-17000 \\ \text { LO_beta:= }-17000 \\ \text { LI_alpha:= - 12000; } \\ \text { LI_alpha }:=-12000 \\ \text { I.]_beta:=0; } \\ \text { I.I_beta }:=0 \\ x A:=(1-x B) \\ x A:=1-x B \\ R:=8.314 \\ R:=8.314 \\ G a:=x A \cdot(\text { Ga_alpha })+x B \cdot\left(G b \_a l p h a ight) \cdot x B+R \cdot T \cdot(x A \cdot \ln (x A)+x B \cdot \ln (x B))+x A \cdot x B \\ \left.\text { - } \text { Lo_alpha }+(x A-x B) \cdot I I \_a l p h a ight) \\ a:=-20000+20000 x B-3000 x B^{2}+7482.600 x B \ln (x B)+7482.600(1-x B) \ln (1-x B) \\ +(1-x B) x B(-27000+24000 x B) \\ G b:=x A \cdot(G a \text { beta })+x B \cdot(G b \text { beta }) \cdot x B+R \cdot T \cdot(x A \cdot \ln (x A)+x B \cdot \ln (x B))+x A \cdot x B \\ \text { - }(L 0 \text { beia }+(x A-x B) \cdot L 1 \text { beta }) \\ f b:=-2000+2000 x B-25000 x B^{2}+7482.600 x B \ln (x B)+7482.600(1-x B) \ln (1-x B) \\\end{array} \)