  In this work, we investigate the relationship between the geometrical
properties, the photon sphere, the shadow, and the eikonal quasinormal modes of
electrically charged black holes in 4D Einstein-Gauss-Bonnet gravity.
Quasinormal modes are complex frequency oscillations that are dependent on the
geometry of spacetime and have significant applications in studying black hole
properties and testing alternative theories of gravity. Here, we focus on the
eikonal limit for high frequency quasinormal modes and their connection to the
black holes geometric characteristics. To study the photon sphere, quasinormal
modes, and black hole shadow, we employ various techniques such as the WKB
method in various orders of approximation, the Poschl-Teller potential method,
and Churilova's analytical formulas. Our results indicate that the real part of
the eikonal quasinormal mode frequencies of test fields are linked to the
unstable circular null geodesic and are correlated with the shadow radius for
an Charged Einstein-Gauss-Bonnet 4D black hole. Furthermore, we found that the
real part of quasinormal modes, the photon sphere and shadow radius have a
lower value for charged black holes in 4D Einstein-Gauss-Bonnet gravity
compared to black holes without electric charge and those of static black holes
in general relativity. Additionally, we explore various analytical formulas for
the photon spheres and shadows, deducing an Churilova's approximate formula for
the black hole shadow radius of the Charged Einstein-Gauss-Bonnet 4D black
hole, which arises from its connection with the eikonal quasinormal modes.
