Sunday, January 11, 2015

Geometry Problem 1073: Triangle, Altitudes, Exterior Point, Distance, Ratio

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 1073: Triangle, Altitudes, Exterior Point, Distance, Ratio.

Posted by Antonio Gutierrez at 1:23 PM
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2 comments:

  1. Jacob HA (EMK2000)January 11, 2015 at 4:27 PM

    Let S(ABC) be the area of ABC.

    S(PBC) − S(PAC) + S(PAB) = S(ABC)
    S(PBC)/S(ABC) − S(PAC)/S(ABC) + S(PAB)/S(ABC) = 1
    pa/ha − pb/hb + pc/hc = 1

    ReplyDelete
  2. AnonymousMay 30, 2015 at 3:07 AM

    P not an arbitrary exterior point, but also in the open convex set between the BA and BC rays. P could be an interior point of the BC side too.

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