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 

(A) Equilateral triangle 

(B) Scalene triangle 

(C) Right-angled triangle 

(D) Isosceles triangle

Answer 1

(A) Equilateral triangle

m(arc AB) + m(arc BC) + m(arc AC) = 360° [Measure of a circle is 360°] 

∴ 120° + 120° + m (arc AC) = 360°

∴ m(arc AC) = 120° 

∴ arc AB = arc BC = arc AC 

∴ seg AB ≅ seg BC ≅ seg AC [Corresponding chords of congruents arcs of a circle are congruent] 

∴ ∆ABC is an equilateral triangle.