Geometry Problem
Click the figure below to see the complete problem 487 about Intersecting Circles, Area, Diameter, Parallel, 90 Degrees.
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Complete Problem 487
Level: High School, SAT Prep, College geometry
Friday, July 30, 2010
Problem 487: Intersecting Circles, Area, Diameter, Parallel, 90 Degrees
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If the radius of the smaller circle is r then the radius of the larger circle is √2r and thus A1 = (1/2)(∏/2)(√2r )^2 - (1/2)(√2r )^2 = ∏r^2/2 - r^2 while sector DCF + A2 =(1/2)(2r)(r)=r^2 and Sector DCF + A3 = ∏r^2/2. Thus A1+A2 +Sector DCF = ∏r^2/2 - r^2 +r^2 = ∏r^2/2 = DCF + A3 or A1 + A2 = A3
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