Points A,B,C are on a circle,
such that m(arcAB)=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
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Solution
Answer: (A) m(arcAB)+m(arcBC)+m(arcAC)=360∘ [Measure of a
circle is 360∘] ∴120∘+120∘+m(arcAC)=360∘ ∴m(arcAC)=120∘ ∴arcAB=arcBC=arcAC ∴segAB≅segBC≅segAC [Corresponding chords of
congruents arcs of a circle are congruent] ∴△ABC is an equilateral triangle.