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(ABKD)=(CEKF) when ABCD #

Source: VIII - Mathematics Regional Olympiad of Mexico Northeast 2008 P1

September 17, 2022
geometryareasparallelogram

Problem Statement

Let ABCDABCD be a parallelogram, EE a point on the line ABAB, beyond B,FB, F a point on the line ADAD, beyond DD, and KK the point of intersection of the lines EDED and BFBF. Prove that quadrilaterals ABKDABKD and CEKFCEKF have the same area.
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