  Let $K_{\lambda}$ be the attractor of the following IFS \begin{equation*}
\{f_1(x)=\lambda x, f_2(x)=\lambda x+1-\lambda\}, \;\;0<\lambda<1/2.
\end{equation*} Given $\alpha \geq 0$, we say the line $y=\alpha x$ is visible
through $K_{\lambda}\times K_{\lambda}$ if $$ \{(x, \alpha x): x\in \mathbb
R\setminus \{0\}\}\cap ((K_{\lambda}\times K_{\lambda}))=\emptyset. $$ Let
$V=\left \{\alpha \geq 0: y=\alpha x \mbox{ is visible through }
K_{\lambda}\times K_{\lambda} \right \}$. In this paper, we give a completed
description of $V$, e.g., its Hausdoff dimension and its topological property.
Moreover, we also discuss another type of visible problem which is related to
the slicing problem.
