2021 · Q13
AB and CD are the diameters of a circle which intersect at P. Join AC, CB, BD and DA. If ∠PAD = 60°, then what is ∠BPD equal to?
Elementary MathematicsCircles
- A30°
- B60°
- C90°
- D120°
Explanation
P is the centre of the circle (intersection of two diameters). In △APD, AP = PD (radii) and ∠PAD = 60°, so it is equilateral and ∠APD = 60°. ∠BPD is supplementary to ∠APD along the straight line APB: 180° − 60° = 120°. Hence option D.