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Topic: feet of altitudes and angles
Replies: 5   Last Post: Dec 1, 1997 12:41 AM

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Barry Wolk

Posts: 42
Registered: 12/6/04
Re: feet of altitudes and angles
Posted: Nov 27, 1997 9:12 PM
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> Prove that the angles formed by connecting the feet of the
> altitudes of a
> triangle are themselves bisected by the altitudes.

In fact, you don't need 3 altitudes -- one is enough.

In an acute triangle ABC, let M be the point on BC such that
AM is an altitude. Let P be any point on AM, let BP meet AC
at Q, and let CP meet AB at R. Then AM bisects angle QMR,
even if BQ and CR are not altitudes.
Barry Wolk | Did you know that the word "pizza"
Dept of Mathematics | is a mathematical formula? It is
University of Manitoba | the volume of a circular pizza of
Winnipeg Manitoba Canada | radius "z" and thickness "a".

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