Geometry Problem. Post your solution in the comments box below.

Level: Mathematics Education, High School, Honors Geometry, College.

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## Sunday, January 11, 2015

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

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Let S(ABC) be the area of ABC.

ReplyDeleteS(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

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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