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TOT 384 1993 Autumn A J2 equal sums of areas of pairs of quads

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June 12, 2024
geometryareas

Problem Statement

The square PQRS PQRS is placed inside the square ABCDABCD in such a way that the segments APAP, BQBQ, CRCR and DSDS intersect neither each other nor the square PQRSPQRS. Prove that the sum of areas of quadrilaterals ABQPABQP and CDSRCDSR is equal to the sum of the areas of quadrilaterals BCRQBCRQ and DAPSDAPS.
(Folklore)
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