O-excircles $(I_a), (I_b), (I_c)$ of $\triangle OBC, \triangle OCA, \triangle OAB.$ $(I_b), (I_c)$ are tangent at $X \in OA,$ $(I_c), (I_a)$ are tangent at $Y \in OB,$ $(I_a), (I_b)$ are tangent at $Z \in OC,$ so that $OX = OY = OZ = p.$ Let $(I_a), (I_b), (I_c)$ touch $BC, CA, AB$ at $U, V, W.$ $OC$ is radical axis of $(I_a), (I_b)$ $\Longrightarrow$ $OA + CA = OX + CV = OY + CU = OB + CB$ $\Longrightarrow$ $OACB$ is tangential with an excircle $(E).$ Internal homothety axis $AB$ of $(E), (I_a), (I_b)$ goes through the external similarity center $P$ of $(I_a), (I_b).$ Only one tangent of $(I_c)$ from $P$ exists, separating $O, I_c.$