MathDB
Engaging geometry collinearity

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July 5, 2020
geometryparallelogram

Problem Statement

O O is the center of a parallelogram ABCD. ABCD. Let G G on the segment OB OB (excluding its endpoints), N N on the line DC DC and M M on the segment AD AD (excluding its endpoints) such that CN>ND,AM=6MD CN>ND, AM=6MD and so that there exists a natural number n≥3 n\ge 3 such that OB=nGO. OB=nGO. Show that G,M,N G,M,N are collinear if and only if (CNND−6)(n+1)=2. \left( \frac{CN}{ND} -6 \right) (n+1)=2.
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