Question

C is a point on the minor arc AB of the circle, with centre O. Given ∠ACB = x° and ∠AOB = y° express y in terms of x. Calculate x, if ACBO is a parallelogram.

Answer 1

Clearly, major arc AB subtends x° at a point on the remaining part of the circle.
∴ reflex ∠ AOB = 2x°
⇒ 360° - y° = 2x°
⇒ y° = 360° - 2x°

Thus, y = 360° - 2x°
If ACBO is a parallelogram,then
x° = y° i.e., x = y
⇒ x = 360° - 2x
⇒ 3x = 360°
⇒ x = 120°.