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triangle construction given intersectionf of <B,<C bisectors and axis of BC

Source: 2022 Oral Moscow Geometry Olympiad grades 8-9 p2

April 17, 2022
geometryconstruction

Problem Statement

Angle bisectors from vertices BB and CC and the perpendicular bisector of side BCBC are drawn in a non-isosceles triangle ABCABC. Next, three points of pairwise intersection of these three lines were marked (remembering which point is which), and the triangle itself was erased. Restore it according to the marked points using a compass and ruler.
(Yu. Blinkov)