Multiple choice

An equilateral $\Delta ABC$ is inscribed in a circle with centre O. The measure of $\angle BOC$ is :

  1. $110^{\circ}$
  2. $100^{\circ}$
  3. $120^{\circ}$
  4. $130^{\circ}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

In an equilateral triangle, each angle is 60 degrees. The angle subtended by a side at the center is double the angle subtended at the circumference. Thus, angle BOC = 2 * 60 = 120 degrees.

AI explanation

By the Inscribed Angle Theorem, the central angle is twice the inscribed angle that subtends the same arc. Because triangle ABC is equilateral, each interior angle is 60 degrees. Therefore, the central angle BOC = 2 * 60 = 120 degrees. The correct option is C.

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