2018 · Q99
In the figure given below, SPT is a tangent to the circle at P and O is the centre of the circle. If ∠QPT = α, then what is ∠POQ equal to?
Elementary MathematicsCircles
- Aα
- B2α
- C90° - α
- D180° - 2α
Explanation
By the alternate segment theorem, the angle between tangent SPT and chord PQ equals the angle in the alternate segment, α. The central angle subtending the same chord is twice the inscribed angle, so ∠POQ = 2α, option (B).