Question

Points A, B, C are on a circle, such that m(arcAB)=m(arcBC)=120°. No point, except point B, is common to the arcs. Which is the type of ΔABC?Choose the correct alternative.
(A) Equilateral triangle
(B) Scalene triangle
(C) Right angled triangle
(D) Isosceles triangle

Answer 1

Answer:

Equilateral triangle

Step-by-step explanation:

m(arcAB) = 120°

=> ∠AOB = 120°  where O is the center of circle

AO = BO = Radius

=> ∠OAB = ∠OBA = (180° - 120°)/2 = 30°

Similarly

∠BOC = 120°

∠OBC = ∠OCB = (180° - 120°)/2 = 30°

∠AOB + ∠BOC + ∠COA = 360°

=> ∠COA = 120°

=> => ∠OAC = ∠OCA = (180° - 120°)/2 = 30°

in ΔABC

∠A = ∠OAB + ∠OAC = 30° + 30° = 60°

Similarly ∠B =  ∠C = 60°

=> ΔABC is   Equilateral triangle

Answer 2

Answer:

equilateral triangle