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Turkey TST 1994 - P4

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March 13, 2011
ratiogeometrygeometry proposed

Problem Statement

Let P,Q,RP,Q,R be points on the sides of △ABC\triangle ABC such that P∈[AB],Q∈[BC],R∈[CA]P \in [AB],Q\in[BC],R\in[CA] and ∣AP∣∣AB∣=∣BQ∣∣BC∣=∣CR∣∣CA∣=k<12\frac{|AP|}{|AB|} = \frac {|BQ|}{|BC|} =\frac{|CR|}{|CA|} =k < \frac 12 If GG is the centroid of △ABC\triangle ABC, find the ratio Area(△PQG)Area(△PQR)\frac{Area(\triangle PQG)}{Area(\triangle PQR)} .
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