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|DAQ|^2 = |PAQ| x |BCD| , ABCD #

Source: 2023 NZMO - New Zealand Maths Olympiad Round 1 p2

September 2, 2023
parallelogramareasarea of a trianglegeometry

Problem Statement

Let ABCDABCD be a parallelogram, and let PP be a point on the side ABAB. Let the line through PP parallel to BCBC intersect the diagonal ACAC at point QQ. Prove that ∣DAQ∣2=∣PAQ∣×∣BCD∣,|DAQ|^2 = |PAQ| \times |BCD| , where ∣XYZ∣|XY Z| denotes the area of triangle XYZXY Z.
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