A circle has centre O and radius 2. A, B and C are points on the circumference of the circle such that AB is the perpendicular bisector of OC.
Find the area of the segment of the circle bounded by the line segment AB and the minor arc ACB.
Give the area in an exact form in terms of surds and (Pi).
This is the diagram I've annotated
It's been awhile since I've done circles but as I remember, there 2 equations to work them out is:
Area of segment AB
r(squared)/2 * ( (Pi)/180 * AngleC - Sin AngleC )
Length of arc ACB
r ( 2 (Pi) AngleC / 360 )
What else can I use to work out what AngleC is, or is my equation going to give the answer as
Area AB = ( (Pi)/90 * AngleC - 2 * Sin AngleC )
Arc ACB = ( (Pi)AngleC )/90
Help is much appreciated.