Inner Triangle

 The Problem:

A point P is chosen somewhere on the base AB of the triangle shown below.

A line parallel to AC is drawn from P to meet BC at Q.

Then a line parallel to BA is drawn from Q to meet AC at R.

R is joined to P to form an ‘inner’ triangle PQR. 

 Where should point P be placed in order to make the area of DPQR as big as possible ?

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Last modified: June 18, 2007