A K Upadhyay and S Upadhyay Solutions for Chapter: Circles, Exercise 1: EXERCISE

In figure, $\mathrm{A}\mathrm{O}\mathrm{C}$ is a diameter of the circle and arc $\mathrm{arc} \mathrm{A}\mathrm{X}\mathrm{B}=\frac{1}{2}\mathrm{a}\mathrm{r}\mathrm{c} \mathrm{B}\mathrm{Y}\mathrm{C}$. Find $\mathrm{\angle }\mathrm{B}\mathrm{O}\mathrm{C}.$

In figure, $\mathrm{X}\mathrm{Y}$ is a diameter of the circle. $\mathrm{P}\mathrm{Q}$ is a chord equal to the radius of the circle. $\mathrm{X}\mathrm{P}$ and $\mathrm{YQ}$ when extended intersect at a point $\mathrm{R}$, find $\mathrm{\angle }\mathrm{X}\mathrm{R}\mathrm{Y}$.

In figure, $\mathrm{O}$ is the centre $\mathrm{A}\mathrm{E}$ is the diameter of the semicircle $\mathrm{A}\mathrm{B}\mathrm{C}\mathrm{D}.$ If $\mathrm{A}\mathrm{B}=\mathrm{B}\mathrm{C}$ and $\mathrm{\angle }\mathrm{A}\mathrm{E}\mathrm{C}={50}^{\mathrm{o}}$, then find $\angle CBE$.

In figure, $\mathrm{O}$ is the centre $\mathrm{A}\mathrm{E}$ is the diameter of the semicircle $\mathrm{A}\mathrm{B}\mathrm{C}\mathrm{D}.$ If $\mathrm{A}\mathrm{B}=\mathrm{B}\mathrm{C}$ and $\mathrm{\angle }\mathrm{A}\mathrm{E}\mathrm{C}={50}^{\mathrm{o}}$, then find $\angle CDE$.

In figure, $\mathrm{O}$ is the centre $\mathrm{A}\mathrm{E}$ is the diameter of the semicircle $\mathrm{A}\mathrm{B}\mathrm{C}\mathrm{D}.$ If $\mathrm{A}\mathrm{B}=\mathrm{B}\mathrm{C}$ and $\mathrm{\angle }\mathrm{A}\mathrm{E}\mathrm{C}={50}^{\mathrm{o}}$, then find $\angle AOB$.

In the given figure, $\mathrm{O}$ is the centre of the circle and $\mathrm{\angle }\mathrm{A}\mathrm{B}\mathrm{P}={42}^{\mathrm{o}}.$ Calculate the measure of $\mathrm{\angle }\mathrm{P}\mathrm{Q}\mathrm{B}$.

In the given figure, $\mathrm{O}$ is the centre of the circle and $\mathrm{\angle }\mathrm{A}\mathrm{B}\mathrm{P}={42}^{\mathrm{o}}.$ Calculate the measure of $\mathrm{\angle }\mathrm{Q}\mathrm{P}\mathrm{B}+\mathrm{\angle }\mathrm{P}\mathrm{B}\mathrm{Q}$.

In figure, $\mathrm{A}\mathrm{B}\mathrm{C}\mathrm{D}$ is a square and $\mathrm{O}\mathrm{A}\mathrm{B}$ is an equilateral $∆.$ Find $\text{'}{x}^{\text{'}}.$