$\quad O$ is the point of intersection of two chords $A B$ and CD of a circle.\ If $\angle B O C=80

Question

$\quad O$ is the point of intersection of two chords $A B$ and CD of a circle.\ If $\angle B O C=80^{\circ}$ and $O A=O D$ then $	riangle O D A$ and $	riangle O B C$ are\

Professor PC Thomas Classes · Answer

(b) $: \angle B O C=80^{\circ}$\ [Given]\ Also, $\angle D O A=\angle B O C=80^{\circ} \quad$ [Vertically opposite angles] $$ O D=O A $$ [Given]\ $\Rightarrow \quad \angle O D A=\angle O A D=\frac{180^{\circ}-80^{\circ}}{2}=50^{\circ}$\ [ ∵ Angles opposite to equal sides in a triangle are equal] $\angle O A D=\angle O C B=50^{\circ}$ and $\angle O D A=\angle O B C=50^{\circ} \quad[\because$ Angles in same segment $]$\ $	herefore \quad 	riangle O D A \sim 	riangle O B C$ and are isosceles.\