Question

Three bus-stops situated at A, B and C in the following figure are operated by handicapped person. These three bus − stops are equidistant from each other. OB is the bisector of ∠ABC and OC is the bisector of ∠ACB.



(i) Find ∠BOC.

(ii) Do you think employment provided to handicapped persons is important for the development of the society? Express your views with relevant points.

Answer 1

(i) In the figure, AB = BC = CA.

∴ ∆ABC is an equilateral triangle.

⇒ ∠ABC = ∠ACB = ∠BAC = 60º

It is given that OB is the bisector of ∠ABC.

∴ ∠ABO = ∠OBC = $\frac{1}{2}\angle \mathrm{ABC}=\frac{1}{2}\times 60°=30°$ .....(1)

Also, OC is the bisector of ∠ACB.

∴ ∠ACO = ∠OCB = $\frac{1}{2}\angle \mathrm{ACB}=\frac{1}{2}\times 60°=30°$ .....(2)

In ∆OBC,

∠OBC + ∠OCB + ∠BOC = 180º (Angle sum property)

⇒ 30º + 30º + ∠BOC = 180º

⇒ ∠BOC = 180º − 60º = 120º

(ii) Yes, the employment provided to handicapped persons is important for the development of the society as employment to handicapped persons provide them with better opportunities of success and prosperity. It helps in their social and economic growth which in turns helps in the development of society.