Uttar Pradesh Board Solutions for Chapter: Circle and Cyclic Quadrilateral, Exercise 6: Efficiency practice 13

$\mathrm{O}$ 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 $\angle \mathrm{ADC}$.

The length of a chord of a circle is equal to its radius. Give the value of the angle made by the chord at the centre. 

Draw a circle of radius $2.5 \mathrm{cm}$. Draw a chord at a distance $0.7 \mathrm{cm}$ from the center of this circle. Find out the length of this chord.

Draw a circle of radius $3.0 \mathrm{cm}$. Draw two chords $\mathrm{AB}$ and $\mathrm{CD}$ of the circle in which $\mathrm{AB}=\mathrm{CD}=3 \mathrm{cm}$. Measure the angles made by each chord at the centre. Are the values of both the angles equal? 

$\angle \mathrm{PQR}=100°$ in the following figure, where $\mathrm{P}, \mathrm{Q}$ and $\mathrm{R}$ are points on a circle with center $\mathrm{O}$. Find $\angle \mathrm{OPR}$