Question

An equilateral triangle △EQU is inscribed in circle centered at O. Then m(arc EQ)=.60∘90∘120∘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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