MathDB

5

Part of 2003 Oral Moscow Geometry Olympiad

Problems(1)

concurrency wanted, centers of 3 rectangles related, wrt a triangle

Source: 2003 Oral Moscow Geometry Olympiad grade 9 p5

10/26/2020
Given triangle ABCABC. Point O1O_1 is the center of the BCDEBCDE rectangle, constructed so that the side DEDE of the rectangle contains the vertex AA of the triangle. Points O2O_2 and O3O_3 are the centers of rectangles constructed in the same way on the sides ACAC and ABAB, respectively. Prove that lines AO1,BO2AO_1, BO_2 and CO3CO_3 meet at one point.
geometryrectangleconcurrencyconcurrent