Multiple choice

An equilateral triangle ABC is inscribed in a circle with centre O. D is a point on the minor arc BC and (\angle CBD = 40^\circ). Find the measure of (\angle BCD).

  1. $30^\circ$
  2. $50^\circ$
  3. $20^\circ$
  4. $40^\circ$
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C Correct answer
Explanation

Since ABC is an equilateral triangle inscribed in a circle, all angles are 60°. Point D lies on minor arc BC. In cyclic quadrilateral ABDC, angle A + angle D = 180°. Given angle CBD = 40°, and angle ABC = 60°, we get angle ABD = 20°. Using properties of cyclic quadrilaterals and inscribed angles, angle BCD = 20°.

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