Online Geometry theorems, problems, solutions, and related topics.
Geometry Problem. Post your solution in the comment box below.Level: Mathematics Education, High School, Honors Geometry, College.Click the figure below to view more details of problem 1251.
https://goo.gl/photos/4guoy5kN3aqGP59PADraw circle O1 diameter GB and circle O2 diameter HBNote that circle O1 pass through points F and DCircle O2 pass through points F and EWe have ∠( GBF)= ∠(GDF)= x∠(FBH)= ∠(FEH)=yBut ∠(FEC)= ∠(FDC)=yBut ∠(GDF)+ ∠(FDC)=90= x+ySo ∠ (GBH)= ∠(GBF)+ ∠(FBH)=x+y=90
Note that GBDF, AEDF and BEFH are all cyclic quadrilaterals. Hence < GBF = < GDF = < AEF = < BHFSo < GBH = < GBF + < HBF = < BHF + <HBF = 90Sumith PeirisMoratuwaSri Lanka