In the figure, given alongside, $\mathrm{AOB}$is a diameter of the circle and $\angle \mathrm{AOC}=110°.$ Find $\angle \mathrm{BDC}$

 

In the following figure, $\mathrm{O}$ is the centre of the circle, $\angle \mathrm{AOB}=60°$ and $\angle \mathrm{BDC}=100°$ Find $\angle \mathrm{OBC}.$

$\mathrm{ABCD}$is a cyclic quadrilateral in which $\angle \mathrm{DAC}=27°;\angle \mathrm{DBA}$ $=50°$ and $\angle \mathrm{ADB}$ $=33°.$ Calculate :

$\angle \mathrm{DBC},$

$\mathrm{ABCD}$is a cyclic quadrilateral in which $\angle \mathrm{DAC}=27°;\angle \mathrm{DBA}$ $=50°$ and $\angle \mathrm{ADB}$ $=33°.$ Calculate :

$\angle \mathrm{DCB},$

$\mathrm{ABCD}$is a cyclic quadrilateral in which $\angle \mathrm{DAC}=27°;\angle \mathrm{DBA}$ $=50°$ and $\angle \mathrm{ADB}$ $=33°.$ Calculate :

$\angle \mathrm{CAB}.$

In the figure given alongside, $\mathrm{AB}$ and $\mathrm{CD}$are straight lines through the centre $\mathrm{O}$ of $\mathrm{a}$ circle. If $\angle \mathrm{AOC}=$ $80°$ and $\angle \mathrm{CDE}=$ $40°,$ find the number of degrees in :

$\angle \mathrm{DCE},$

In the figure given alongside, $\mathrm{AB}$ and $\mathrm{CD}$are straight lines through the centre $\mathrm{O}$ of $\mathrm{a}$ circle. If $\angle \mathrm{AOC}=$ $80°$ and $\angle \mathrm{CDE}=$ $40°,$ find the number of degrees in :

$\angle \mathrm{ABC}.$

In the given figure, $\mathrm{AC}$ is a diameter of a circle, whose centre is $\mathrm{O}.$

Circle is described on $\mathrm{AO}$as diameter. $\mathrm{AE}$, a chord of the larger circle, intersects the smaller circle at $\mathrm{B}.$

 Prove that: $\mathrm{AB}=\mathrm{BE}.$

In the following figure,

if $\angle \mathrm{BAD}=96°,$ find $\angle \mathrm{BCD}$ and $\angle \mathrm{BFE}.$