Question

Prove that The angle which an arc of a circle subtends at the centre is double the angle which it subtends at any point on the remaining part of the circumference.

Answer 1

Data:

Arc AMB subtends ∠AOB at the centre O of the circle ∠APB on the remaining part of the circumference.

To Prove:

∠AOB = 2 ∠APB

Construction:

Join PO and produce it to Q. Let ∠APQ = x and ∠BPQ=y.

Proof: