Question

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

• A. 60${}^{\circ }$
• B. 90${}^{\circ }$
• C. 120${}^{\circ }$
• D. 150${}^{\circ }$

Answer 1

The correct option is C 120${}^{\circ }$

$△EQU$ 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${}^{\circ }$
$⟹$ 3x = 360${}^{\circ }$
$⟹$ x = 120${}^{\circ }$