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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

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Solution

Answer: (A)
m(arcAB)+m(arcBC)+m(arcAC)=360 [Measure of a
circle is 360]
120+120+m(arc AC)=360
m(arcAC)=120
arc AB=arc BC=arc AC
segABsegBCsegAC [Corresponding chords of
congruents arcs of a circle are congruent]
ABC is an equilateral triangle.

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