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°, then find angle B O C.

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°, then find angle B O C. (A) 60° (B) 80° (C) 100° (D) 120°

Tardigrade Admin · Accepted Answer

(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°.

Q. In the given figure, (not to scale), rectangle $A BC D$ and triangle $A BE$ are inscribed in the circle with centre $O$ . If $∠ A EB = 4 0^{\circ}$ , then find $∠ BOC$ .

$6 0^{\circ}$

$8 0^{\circ}$

$10 0^{\circ}$

$12 0^{\circ}$

(i) Join $O A$ and use properties of arcs.
(ii) $∠ A OB = 2∠ A EB$ .
(iii) $A OC$ is the diameter, i.e., $∠ A OB + ∠ BOC =$ $18 0^{\circ}$ .

Q. In the given figure, (not to scale), rectangle ABCD and triangle ABE are inscribed in the circle with centre O. If ∠AEB=40∘, then find ∠BOC.

60∘

80∘

100∘

120∘