  The LHCb collaboration reported the observation of a narrow peak in the $D^-
K^+$ invariant mass distributions from the $B^+\to D^+ D^- K^+$ decay. The peak
is parameterized in terms of two resonances $X_0(2900)$ and $X_1(2900)$ with
the quark contents $\bar{c}\bar{s}ud$, and their spin-parity quantum numbers
are $0^+$ and $1^-$, respectively. We investigate the rescattering processes
which may contribute to the $B^+\to D^+ D^- K^+$ decays. It is shown that the
$D^{*-}K^{*+}$ rescattering via the $\chi_{c1}K^{*+}D^{*-}$ loop or the
$\bar{D}_{1}^{0}K^{0}$ rescattering via the $D_{sJ}^{+}\bar{D}_{1}^{0}K^{0}$
loop simulate the $X_0(2900)$ and $X_1(2900)$ structures. Such phenomena are
due to the analytical property of the scattering amplitudes with the triangle
singularities located to the vicinity of the physical boundary.
