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An acute angle and a point inside it are given

Source: Balkan MO 1994, Problem 1

April 25, 2006
geometryparallelogramanalytic geometrytrigonometryparameterizationconicsparabola

Problem Statement

An acute angle XAYXAY and a point PP inside the angle are given. Construct (using a ruler and a compass) a line that passes through PP and intersects the rays AXAX and AYAY at BB and CC such that the area of the triangle ABCABC equals AP2AP^2. Greece
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