Hey guys. I'm studying maths at AS-level, and just finished the unit on circles. We learnt about completing the square to get the radius, centre co-ordinates etc. We also did the equation of a tangent too, that's about as much as the chapter covered. I like a challenge so asked my teacher for some extension questions; this is the hardest one I have ever been given. Could someone begin to explain how to go about this simply without incredibly long formulas and actually talk me through the process? Thanks guys.
'The region R is the intersection of the interiors of the two circles given by x^2 + y^2 = a^2 and x^2 + y^2 = 2ax + 2ay - a^2 where a >= 0. Find the value of a such that the area of R is (pi)-2.'
My teacher told me the area of overlapping circles is called a 'lens' and I'm thinking it could have something to do with subtracting the area of a sector from the area of the triangle with the chord between the two intersecting points as the base. Please help.
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