Math CentralQuandaries & Queries


Question from Bibi, a student:

An equilateral triangle has a point P inside it. PA, PB, PC are the perpendiculars from point P to the three sides of the triangle. Help me show that PA+PB+PC is the same no matter where the point P is..?

Hi Bibi,


I called the triangle LMN and joined P to each of the vertices. Hence triangle LMN is partitioned into three triangles, LMP, NP and NLP. What are the areas of these three triangles?


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