Proposed Problem

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Complete Problem 316

Level: High School, SAT Prep, College geometry

## Wednesday, July 8, 2009

### Problem 316: Circular segments and Inscribed Squares

Labels:
circular segment,
perpendicular,
side,
square

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Draw OQ parallel to AB meeting EF in Q. Thus, OQ=a/2 and QF=a-x. We've ON^2=(b/2)^2+(b+x)^2 & OF^2=(a/2)^2+(a-x)^2 but ON = OF being the radii of the circle. So,(b/2)^2+(b+x)^2=(a/2)^2+(a-x)^2 which, on simplification, directly yields x=5(a-b)/8

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