R S Aggarwal and Veena Aggarwal Solutions for Exercise 2: EXERCISE 12B

In the adjoining figure, chords$\mathrm{AC}$ and $\mathrm{BD}$ of a circle with centre $\mathrm{O}$ intersect at right angles at $\mathrm{E}$ If $\angle \mathrm{OAB}={25}^{\circ }$ calculate $\angle E\mathrm{BC}$.

In the given figure, $\mathrm{O}$ is the center of a circle in which$\angle \mathrm{OAB}=20°\text{ and }\angle \mathrm{OCB}=55°$Find

In the given figure, $\mathrm{O}$ is the centre of a circle in which$\angle \mathrm{OAB}=20°\text{ and }\angle \mathrm{OCB}=55°$. Find $\angle \mathrm{AOC}$.

In the given figure, $O$ is the centre of the circle and $\angle BCO=30°$. Find $x$ and $y.$

In the given figure, $O$ is the centre of the circle, $BD=OD$ and $CD \perp AB.$ Find $\angle CAB.$

In the given figure, $\mathrm{PQ}$ is a diameter of a circle with center $\mathrm{O}$ If$\angle \mathrm{POR}=65°,\angle \mathrm{SPR}=40°\text{ and }\angle \mathrm{POM}=50°$. If $\angle Q\mathrm{PR}=x°,\angle Q\mathrm{PM}=y°, \text{and }\angle \mathrm{PRS}=z°$, then find the value of $x+y+z$.  

 In the figure given below, $P$ and $Q$ are centres of two circles, intersecting at $B$ and $C,$ and $ACD$ is a straight line. If $\angle APB =$$150°$ and $\angle BQD=x^0$ find the value of $x.$

In the given figure, $AB$ and $CD$ are two chords of a circle, intersecting each other at a point $E.$ Prove that $\angle AEC =$ $\frac{1}{2}$ (angle subtended by arc $CXA$ at the centre $+$ angle subtended by arc $DYB$ at the centre).