Question

Points A, B, C are on a circle, such that m(arc AB) = m(arc BC) = 120°. No point, except point B, is common to the arcs. Which is the type of ∆ABC?

Options

• Equilateral triangle 

• Scalene triangle 

• Right angled triangle 

• Isosceles triangle 

Answer 1

Equilateral triangle 

Explanation:

m(arc AB) = m(arc BC) = 120º

Now, m(arc AB) + m(arc BC) + m(arc CA) = 360º 

⇒ 120º + 120º + m(arc CA) = 360º

⇒ 240º + m(arc CA) = 360º

⇒ m(arc CA) = 360º – 240º = 120º

∴ m(arc AB) = m(arc BC) = m(arc CA)

⇒ arc AB ≅ arc BC ≅ arc CA.   ...(Two arcs are congruent if their measures are equal)

⇒ chord AB ≅ chord BC ≅ chord CA.   ...(Chords corresponding to congruent arcs of a circle are congruent)

∴ ∆ABC is an equilateral triangle.   ...(All sides of equilateral triangle are equal)

Hence, the correct answer is option Equilateral triangle.