MathDB
2020 Geometry 5

Source:

February 2, 2020
geometry2020

Problem Statement

For every positive integer kk, let Tk=(k(k+1),0)\mathbf{T}_k = (k(k+1), 0), and define Hk\mathcal{H}_k as the homothety centered at Tk\mathbf{T}_k with ratio 12\tfrac{1}{2} if kk is odd and 23\tfrac{2}{3} is kk is even. Suppose P=(x,y)P = (x,y) is a point such that (H4∘H3∘H2∘H1)(P)=(20,20).(\mathcal{H}_{4} \circ \mathcal{H}_{3} \circ \mathcal{H}_2 \circ \mathcal{H}_1)(P) = (20, 20). What is x+yx+y? (A homothety H\mathcal{H} with nonzero ratio rr centered at a point PP maps each point XX to the point YY on ray PX→\overrightarrow{PX} such that PY=rPXPY = rPX.)
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