Question

Three bus-stops situated at A,B andC in a fig operated by handicapped person. These three bus stop equidistant from each other. OB is the bisector of angle ABC and OC is the bisector of angle ACB.find angle BOC

Answer 1

Answer:Since, A, B, C are equidistant from each other.

∴  ∠ABC is an equilateral triangle.

⇒ ∠ABC = ∠ACB = 60°  

⇒ ∠OBC = ∠OCB = 1/2 x 60 = 30° (Since, OB and OC are angle bisectors)

Now, ∠BOC = 180° - ∠OBC - ∠OCB (Using angle sum property of triangle)

⇒ ∠BOC = 180° - 30° - 30° = 120°

Step-by-step explanation:

Answer 2

Answer:

Step-by-step explanation:

Given: Points A, B and C are equidistant from each other. OB is the bisector of ∡ABC and OC is the bisector of ∠ACB

Since, A, B, C are equidistant from each other.

∴  ∠ABC is an equilateral triangle.

⇒ ∠ABC = ∠ACB = 60°  

⇒ ∠OBC = ∠OCB = 1/2 x 60 = 30° (Since, OB and OC are angle bisectors)

Now, ∠BOC = 180° - ∠OBC - ∠OCB (Using angle sum property of triangle)

⇒ ∠BOC = 180° - 30° - 30° = 120°

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