2021 · Q14
An equilateral triangle ABC and a scalene triangle DBC are inscribed in a circle on same side of the arc. What is ∠BDC equal to?
Elementary MathematicsCircles
- A30°
- B45°
- C60°
- D90°
Explanation
∠BDC and ∠BAC subtend the same chord BC and lie on the same side of it, so by the same-segment theorem they are equal. △ABC is equilateral, so ∠BAC = 60°, giving ∠BDC = 60°. Hence option C. (D cannot lie on the opposite arc since it is on the same side.)