Proposed Problem
Click the figure below to see the complete problem 403 about Circular sector, 90 degrees, Circle, Semicircle, Area.
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Complete Problem 403
Level: High School, SAT Prep, College geometry
Wednesday, December 16, 2009
Problem 403. Circular sector, 90 degrees, Circle, Semicircle, Area
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Let R radius OC and r radius of circle D.
ReplyDeleteLet x distance of D to segment OB. Then x^2 = (R+r)^2-(R-r)^2=4Rr.
Radius OB is equal to 2R, and then:
2R=r+sqrt(x^2+r^2) -> R=2r -> S = (pi/4)*R^2 (1)
A(AOB) = (pi/4)*(2R)^2 - (pi/2)*R^2 = (pi/2)*R^2 = S + S1 + S2 + S3 (2)
By eq (1) and (2), we've: S = A(AOB)/2 = S1 + S2 + S3
MIGUE