MathDB

4

Part of 1974 Poland - Second Round

Problems(1)

sum of areas, 9 parts in a quad

Source: Polish MO Second Round 1974 p4

9/8/2024
In a convex quadrilateral ABCD ABCD with area S S , each side was divided into 3 equal parts and segments were drawn connecting the appropriate points of division of the opposite sides in such a way that the quadrilateral was divided into 9 quadrilaterals. Prove that the sum of the areas of the following three quadrilaterals resulting from the division: the one containing the vertex A A , the middle one and the one containing the vertex C C is equal to S3 \frac{S}{3} .
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