7
Part of 2016 Sharygin Geometry Olympiad
Problems(3)
equal diagonals in ABCD and a few perpendicular bisectors
Source: Sharygin Geometry Olympiad 2016 Final Round problem 7 grade 8
7/22/2018
Diagonals of a quadrilateral are equal and meet at point . The perpendicular bisectors to segments and meet at point , and the perpendicular bisectors to and meet at point . Find angle .by A.Zaslavsky
geometryperpendicular bisectordiagonals
If altitudes form triangle, so do angle bisectors!
Source: Sharygin Geometry Olympiad, Final Round 2016, Problem 7 grade 9
8/4/2016
From the altitudes of an acute-angled triangle, a triangle can be composed. Prove that a triangle can be composed from the bisectors of this triangle.
geometryGeometric Inequalitiestrigonometry
Restoring a triangle
Source: Sharygin geometry olympiad 2016, grade 10, Final Round, Problem 7.
8/5/2016
Restore a triangle by one of its vertices, the circumcenter and the Lemoine's point. (The Lemoine's point is the intersection point of the reflections of the medians in the correspondent angle bisectors)
constructionsymmedian pointCircumcentergeometrycircumcirclegeometric transformationreflection