Question

In the given figure, (not to scale), rectangle $A B C D$ and triangle $A B E$ are inscribed in the circle with centre $O$. If $\angle A E B=40^{\circ}$, then find $\angle B O C$.

• A. $60^{\circ}$
• B. $80^{\circ}$
• C. $100^{\circ}$
• D. $120^{\circ}$

Answer 1

Answer: (C)

(i) Join $O A$ and use properties of arcs.
(ii) $\angle A O B=2 \angle A E B$.
(iii) $A O C$ is the diameter, i.e., $\angle A O B+\angle B O C=$ $180^{\circ}$.