Chapter 10: Circles
Q1. In a circle, the angle at the centre is twice the angle at the circumference subtended by the same arc. Prove this.
SolutionLet arc AB subtend ∠AOB at centre and ∠ACB at circumference.
Draw diameter through O and C.
In ▹OAC: OA = OC (radii)
∠OAC = ∠OCA = x
Exterior angle = 2x
Similarly for ▹OBC
Total: ∠AOB = 2∠ACB ✓