Online Geometry theorems, problems, solutions, and related topics.
Proposed ProblemClick the figure below to see the complete problem 316.See more:Complete Problem 316Level: High School, SAT Prep, College geometry
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