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here i'll just explain the procedure and see if u can do it then.... if not then i'll solve it out for u ... so here goes...MATH A2 PAPER 3 2013 OCTOBER
PLEase reply
the circle with centre O has the radius r ... however the circle with the center A has the radius AB. so first step will be to find AB (radius of the circle with center A)
AB^2 = r^2 + r^2 - 2(r)(r)Cos(pie - 2thita)
this from the cosine rule.... and triangle BOA. u will then get the expression for the length of AB.
the angle (pie-2theeta) comes from the fact that in triangle BOA, OB and OA are equal so angleOBA=angleOAB=theeta
the shaded region is made up of a sector with (center A and radii AB=AC ) and two equal segments.
find the area of the sector BAC from the formula
(2theeta/2pie)*(pie)(AB)^2
Now u have to find the area of the segments. take one segment first.
calculate the area of sector BOA.
calculate the area of triangle BOA.
(area of sector - area of traingle)=area of segment
Area of shaded region = (area of sector BAC) + 2(area of segment)
[(pie)(R)^2]/2 = xyz + 2abc
(xyz and abc are watever areas u get)
If this whole stuf is too confusing then tell me and i'll solve it and try to send u a pic of that. toodles but it will be better if u work through these steps one by one with ur pen and paper in hand and not just read it and become confused as hell