MathDB

4

Part of 2009 Dutch Mathematical Olympiad

Problems(1)

dutch parallelogram, similar triangles on triangle sides

Source: Dutch NMO 2009 p4

9/6/2019
Let ABCABC be an arbitrary triangle. On the perpendicular bisector of ABAB, there is a point PP inside of triangle ABCABC. On the sides BCBC and CACA, triangles BQCBQC and CRACRA are placed externally. These triangles satisfy △BPA∼△BQC∼△CRA\vartriangle BPA \sim \vartriangle BQC \sim \vartriangle CRA. (So QQ and AA lie on opposite sides of BCBC, and RR and BB lie on opposite sides of ACAC.) Show that the points P,Q,CP, Q, C and RR form a parallelogram.
geometryparallelogramsimilar triangles