1

Part of 2005 Oral Moscow Geometry Olympiad

Problems(2)

area bisector in a figure consisted of two joined rectangles

Source: 2005 Oral Moscow Geometry Olympiad grades 8-9 p1

The hexagon has five

90^o

270^o

angle (see picture). Use a straight-line ruler to divide it into two equal-sized polygons. https://cdn.artofproblemsolving.com/attachments/d/8/cdd4df68644bb8e04adbe1b265039b82a5382b.png

geometryareasrectangle

min circumradii wanted, line // BC in triangle ABC

Source: 2005 Oral Moscow Geometry Olympiad grades 10-11 p1

Given an acute-angled triangle

ABC

. A straight line parallel to

BC

intersects sides

AB

AC

M

P

, respectively. At what location of the points

M

P

will the radius of the circle circumscribed about the triangle

BMP

be the smallest?
(I. Sharygin)

geometryradiusparallel