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Question

An equilateral triangle EQU is inscribed in circle centered at O. Then m(arc EQ)=.
  1. 60
  2. 90
  3. 120
  4. 150


Solution

The correct option is C 120
EQU is equilateral. Then all the sides of the triangle are equal. Then EQ = QU = UE.
We know that corresponding arcs of congruent chords of a circle (or congruent circles) are congruent.
Hence, arc EQ, arc QU and arc UE are congruent.
m(arc EQ) = m(arc QU) = m(arc UE)
If m(arc EQ) = x, then
x + x + x = 360
3x = 360
x = 120

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