2012 · Q93
In the figure AB is the diameter of a circle with centre O, and AO = CD where C, D are points on the circle joined to an external point P (A, C, P and B, D, P collinear). What is angle APB equal to?
Elementary MathematicsGeometry
- A60 degrees
- B50 degrees
- C45 degrees
- D30 degrees
Explanation
CD = radius makes triangle OCD equilateral, so arc CD subtends 60 degrees at the centre; the external angle APB = (arc AB - arc CD)/2 = (180-60)/2 = 60 degrees.