R. D. Sharma Solutions for Chapter: Circles, Exercise 5: EXERCISE

In the following figure, $AB$ and $CD$ are diameters of a circle with centre $O$ If $\angle OBD=50°$ find $\angle AOC$.

In a cyclic quadrilateral $ABCD$, if $m\angle A=3(m\angle C)$. Find $m\angle A$.

In the following figure, if $\angle BAC=60°$ and $\angle BCA=20°$ and $\angle ADC=k°$, then find the value of $k$.

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In the following figure, $ABCD$ is a cyclic quadrilateral. Find the value of $x$.

$ABCD$ is a cyclic quadrilateral in which $BC \Vert AD,\angle ADC=110°$,  $\angle BAC=50°$ and $\angle DAC=k°$, then find the value of $k$.

$ABCD$ is a cyclic quadrilateral in which $\angle DBC=80°$ and $\angle BAC=40°$. Find $\angle BCD$. 

$ABCD$ is a cyclic quadrilateral in which:

$\angle BCD=100°$ and $\angle ABD=70°$ find $\angle ADB$.

In the following figure, $ABCD$ is a cyclic quadrilateral in which $AC$ and $BD$ are its diagonals. If $\angle DBC=55°$, $\angle BAC=45°$ and $\angle BCD=k°$, then find the value of $k$.