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areas by cevians (2023 Adygea Teachers' Geometry Olympiad p1-2)

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February 28, 2024
geometryareas

Problem Statement

Three cevians divided the triangle into six triangles, the areas of which are marked in the figure.
1) Prove that S1⋅S2⋅S3=Q1⋅Q2⋅Q3S_1 \cdot S_2 \cdot S_3 =Q_1 \cdot Q_2 \cdot Q_3.
2) Determine whether it is true that if S1=S2=S3S_1 = S_2 = S_3, then Q1=Q2=Q3Q_1 = Q_2 = Q_3.
https://cdn.artofproblemsolving.com/attachments/c/d/3e847223b24f783551373e612283e10e477e62.png
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