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Geometry Problem. Post your solution in the comments box below.Level: Mathematics Education, High School, Honors Geometry, College.Click the diagram below to enlarge it.
Points A ,O1 and O2 are collinearLets line joining A,O1 and O2 intersects BD at E and BC at F. Lets assume angle AO2D = x And angle AO1C = y We can see that Angle BEF = 90 - x And Angle BFE = y - 90And we get Angle EBF = Angle DBC = 180 - (y-x) Also Angle O1AC = 90 - y/2 Angle O1AD = 90 + (x/2) We get angle DAC = 180 - [(y-x)/2] Since O3 is circumcentre of triangle ACD Angle DO3C = y - x It means quad. BCO3D is cyclic and O3 lies on circle O4.