MathDB

2

Part of 2017 Oral Moscow Geometry Olympiad

Problems(2)

incircles in triangles of isosceles trapezoid lead to perpendicularity

Source: 2017 Oral Moscow Geometry Olympiad grades 8-9 p2

7/26/2019
An isosceles trapezoid ABCDABCD with bases BCBC and ADAD is given. Circles with centers O1O_1 and O2O_2 are inscribed in triangles ABCABC and ABDABD. Prove that line O1O2O_1O_2 is perpendicular on BCBC.
geometrytrapezoidisoscelesperpendicularincircle
Geomtery

Source: Sharygin Oral Geometry Olympiad 2017.Senior League(10-11) P2

4/16/2017
Given pyramid with base n−gonn-gon. How many maximum number of edges can be perpendicular to base?
geometry3D geometrypyramid