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Part of 2023 Adygea Teachers' Geometry Olympiad

Problems(1)

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

Source:

2/28/2024
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.
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