Question

In the picture, O is the centre of the circle and A, B, O are points on it. Prove that ​

Answer 1

Answer:

Join A to the centre O of the circle. This line splits the angle at A into two parts, x° and y° .

● Here Δ AOB and Δ AOC are isosceles triangle

Thus, ∠ ABO = ∠ OAB = x° and ∠ ACO = ∠ OAC = y°

● Let us take ∠ BOC = c°

⇒ (180° – 2x) + (180° – 2y) + c° = 360°

⇒ 360° –2 (x+y) +c° = 360°

⇒ 2(x+y) = c°