Problem

Source: 2013 Romania JBMO TST3 P3

Tags: geometry, incircle, external tangent, common tangents, cyclic quadrilateral, parallel



Let $ABCD$ be a cyclic quadrilateral and $\omega_1, \omega_2$ the incircles of triangles $ABC$ and $BCD$. Show that the common external tangent line of $\omega_1$ and $\omega_2$, the other one than $BC$, is parallel with $AD$