Three Parallel Segments

This is based on an idea of Juan Bosco Romero: Let $ABC$ be a triangle with incenter $I$ and circumcenter $O$.
Call $A_b, A_c$ the reflection of $A$ on lines $BI$ and $CI$, respectively. Define $B_c, B_a$ and $C_a, C_b$ analogously.
Then line segments $B_cC_b$, $C_aA_c$ and $A_bB_c$ are parallel. They are also proportional to the sides of $ABC$ and we have the ratios $B_cC_b/BC = C_aA_c/CA = A_bB_a/AB = OI/R$.


The common infinite point of lines $B_cC_b, C_aA_c$ and $A_bB_c$ is the isogonal conjugate of the point $X_{100}$.

SONIA + FRAN = PABLO

Con motivo del nacimiento de Pablo, presento este criptograma en el que cada letra corresponde a uno de los dígitos del 0 al 9, sin que se repita ninguno.

¿Sabrías encontrar alguna de las ocho soluciones? Y claro, ¿por qué no las ocho?