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.

2 comments:

  1. 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

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  2. 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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