Question

In following figure , C is a point on the minor arc AB of the circle with centre O . Given ∠ ACB = p° , ∠  AOB = q° , express q in terms of p. Calculate p if OACB is a parallelogram.

Answer 1

∠ AOB = q 

Reflex ∠ AOB = 360 - q

Since arc AB subtends reflex ∠  AOB = (360 - q)°  at the centre and ∠ ACB on the remaining part of the circle .

∴ ∠ ACB = `1/2` (reflex ∠ AOB)

If OACB is a parallelogram

∠ AOB = ∠ ACB

q = p

360 - 2p = p

3p = 360

 p = 120°