Three friends Amit, Mayank and Richa were playing with ball by standing on a circle at A, B and C point respectively. Richa throws a ball to Amit, Amit to Mayank and Mayank to Richa. They all are equidistant from each other as shown in the figure. Considering O as the centre of the circle, answer the following questions.
(i) What is the measure of ∠BOC?
(ii) What is the value of ∠OBC + ∠OCB?
PLS ANSWER ASAP IF ANYONE KNOWS!!!
Answers & Comments
Answer:
i) 120 degrees
ii) 240 degrees
Given:
AB = BC = CA
To Find:
(i) ∠BOC
(ii) ∠OBC + ∠OCB
Explanation:
In the given figure
AB = BC = CA(Given)
In Δ ABC is equilateral
So, ∠A = ∠B = ∠C = 60°
OA = OB = OC (Radius)
Therefore, ∠BCO = OCB = 30° (Equal sides have equal opposite angles)
Using angle sum property in ΔOBC
∠BCO + BCO + OCB +∠COB =180°
∠BCO + OCB = 60°
∠COB = 120°
Answer = 120° ,60°