Common tangent
= Common tangent
A line tangent to two curves or to a curve at two distinct points. For functions $g_1,g_2$, contact at $x_1,x_2$ requires equal derivatives and equal intercepts: $g_1'(x_1)=g_2'(x_2)=m$ and $g_1(x_1)-mx_1=g_2(x_2)-mx_2$. The <common-tangent construction> uses the lower supporting line for phase coexistence.