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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.
Solution
∠ 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°
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