MathDB

4

Part of 2011 Oral Moscow Geometry Olympiad

Problems(2)

perpendicular passes through midpoint, in trapezoid ABCD, AB = BC = CD

Source: 2011 Oral Moscow Geometry Olympiad grades 8-9 p4

4/17/2020
In the trapezoid ABCD,AB=BC=CD,CHABCD, AB = BC = CD, CH is the altitude. Prove that the perpendicular from HH on ACAC passes through the midpoint of BDBD.
geometrytrapezoidisoscelesmidpointaltitudeperpendicular
rigid flat triangle T with area <4, may be inserted in triangular hole of area 3

Source: 2011 Oral Moscow Geometry Olympiad grades 10-11 p4

4/8/2020
Prove that any rigid flat triangle TT of area less than 44 can be inserted through a triangular hole QQ with area 33.
geometryarea of a triangleareas3D geometry