MathDB

1

Part of 1994 Turkey Team Selection Test

Problems(2)

Turkey TST 1994 - P1

Source:

3/13/2011
ff is a function defined on integers and satisfies f(x)+f(x+3)=x2f(x)+f(x+3)=x^2 for every integer xx. If f(19)=94f(19)=94, then calculate f(94)f(94).
functionalgebra proposedalgebra
Turkey TST 1994 - P4

Source:

3/13/2011
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)} .
ratiogeometrygeometry proposed