Question

C is a point on the minor arc AB of the circle, with centre O. Given ∠ACB = p°, ∠AOB = q°.
(i) Express q in terms of p.
(ii) Calculate p if ACBO is a parallelogram. 
(iii) If ACBO is a parallelogram, then find the value of q + p.

Answer 1

(i) Reflex ∠ AOB = 360° - q°
ACB = `1/2`reflex ∠ AOB     .....(angle at the centre property)

p° = `1/2` (360° - q°)

2p° = 360° - q°
q° = 360° - 2p°
q = 360° - 2p

(ii) If ACBO is a parallelogram, then
p = q
q = 360° - 2p
p = 360° - 2p
p + 2p = 360°
p = `(360°)/3 = 120°`

(iii) If ACBO is a parallelogram, then
p = q
Also, p = 120°         ....(From(ii))
p + q = p + p = 2p
p + q = 2 + 120°= 240°.