Saturday, November 8, 2014

Geometry Problem 1058: Triangle, Sum of the Areas, Altitude, Perpendicular, Circumcircle, Circle, Diameter

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.

Online Math: Geometry Problem 1058: Triangle, Sum of the Areas, Altitude, Perpendicular, Circumcircle, Circle, Diameter.
at

2 comments:

  1. Jacob HA (EMK2000)November 8, 2014 at 10:36 PM

    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

    ReplyDelete
  2. PravinNovember 9, 2014 at 7:32 AM

    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.

    ReplyDelete

Share your solution or comment below! Your input is valuable and may be shared with the community.