Online Geometry theorems, problems, solutions, and related topics.
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.
One can show that BD⊥EF. Then S(BEDF)= 1/2×BD×EF= BO×EF= S(ABC) (by Problem 1055)Thus sobtracting S(BEGMF) both side, S₁+S₂=S₃
Join DA, DC,DH. Let (XYZ) stand for area of ΔXYZ.AD // EH implies (AED) = (AHD). Follows S1 = (GHD).DC // HF implies (DFC) = (DHC). Follows S2 = (MHD).Hence S1 + S2 = S3.