Identify the cyclic quadrilateral in the following shapes:

Identify the cyclic points in the following circle:

The points $\mathrm{A},\mathrm{B},\mathrm{C}$ and $\mathrm{D}$ are cyclic points. 

The points $\mathrm{A},\mathrm{B},\mathrm{C},\mathrm{D}$ and $\mathrm{E}$ are not cyclic points. 

The point $O$ in following figure is the center of the circle. If chord $\mathrm{AC}=$ chord $\mathrm{BC}$ then find the value of $\angle \mathrm{ABC}$ and $\angle \mathrm{ACB}+$ $\angle \mathrm{APB}$.

$\mathrm{O}$ is the center of the circle in the figure. The radius $\mathrm{OD}$ is perpendicular to the diameter $\mathrm{AB}$. If $\mathrm{C}$ is a point on the circle, then find $\angle \mathrm{ABD}$ and $\angle \mathrm{BCD}$. 

In the given figure, there is a cyclic quadrilateral $\mathrm{ABCD}$ inscribed in a circle. Diagonals $\mathrm{AC}$ and $\mathrm{BD}$ are drawn. If $\angle \mathrm{ACB}=55°$ and $\angle \mathrm{BAC}=45°$ then find $\angle \mathrm{ADC}$.