= Solution
At the south pole $\mathbf r=-R\hat z$. Choose plate C as the instantaneous <reference frame>. Since $R=4\times10^9$ mm, the two components of relative angular <speed> give 20 and 48 mm/year. The plate <velocities> in the fixed tangent-plane axes are
$$
\mathbf v_C=(0,0),\qquad\mathbf v_A=(-48,0),\qquad\mathbf v_B=(-48,20)\quad\mathrm{mm\,yr^{-1}}.
$$
The <plate velocity triangle> therefore has sides
$$
\boxed{|\mathbf v_B-\mathbf v_A|=20,\quad|\mathbf v_A-\mathbf v_C|=48,\quad|\mathbf v_B-\mathbf v_C|=52\quad\mathrm{mm\,yr^{-1}}.}
$$
The physical boundary rays point along $+x$ for AB, $+y$ for AC and $(12,-5)$ for BC. Plate A occupies the quadrant between the first two rays, B the narrow wedge between AB and BC, and C the remainder. The stated overriding relations make AB and AC <subduction trenches>, while BC remains a <transform fault>: this is a <trench-trench-transform triple junction>. Put the <subduction> teeth on B's side of AB and A's side of AC, identifying B above A and A above C.
For kinematic stability there must be a single junction <velocity> $\mathbf U$ compatible with all three boundary-normal motions. Use the standard idealization that each trench's normal <velocity> is that of its <overriding plate>, with no independent rollback. AB is parallel to $x$, so $U_y=v_{B,y}=20$. AC is parallel to $y$, so $U_x=v_{A,x}=-48$. The transform requires $\mathbf U-\mathbf v_C$ to be parallel to $(12,-5)$, which is true for this intersection. Hence
$$
\boxed{\mathbf U_S=(-48,20)\,\mathrm{mm\,yr^{-1}}=\mathbf v_B\quad\text{in the C frame}.}
$$
\b[The southern <triple junction> is instantaneously kinematically stable.] It is stationary relative to B, migrates along AB relative to A, and migrates along BC relative to C. This compatibility result does not promise long-term stability if plate <rotations> or trench rollback change. Notice that the three relative <velocities> close even though the overriding order is not a statement that all three plates move toward one common stationary point.
\Image[/past-exam-of-the-physics-of-the-earth-as-a-planet-course-of-the-university-of-cambridge/2016/paper-1-polar-junctions.png]
{title=Original polar boundary geometry and plate velocity triangles; dashed velocity-space constraints locate compatible south and north junction velocities}
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