Trig. segmet area+perimiter
Hi again, i'm currently studying for my pure maths intermediate level exam and i need some help with a trigonometry question please:
The points A and B lie on the circumference of a circle center O and radius
r cm, such that the angle AOB = θ radians. The sector AOB has area 9cm^2 and the total perimeter of sector AOB is 15cm.
a)Show that r satisfies the equation 2r^2 - 15r + 18 = o
b)Find the value of θ,explaining why there is only one possible value.
I know that area of sector = (1/2).(r^2).(θ)
not sure if perimiter of sector would be length of arc + radius x2
Any help is appreciated,thanks!
*sry i meant sector not segment in thread title