4
Problems(2)
midpoint arc construction with no more than two lines
Source: 2018 Oral Moscow Geometry Olympiad grades 8-9 p4
7/25/2019
Given a triangle () and a circle circumscribed around it. Construct with a compass and a ruler the midpoint of the arc (not containing vertex ), with no more than two lines (straight or circles).
arc midpointconstructiongeometry
segments of midpoints of incenters and excenters perpendicular to side
Source: 2018 Oral Moscow Geometry Olympiad grades 10-11 p4
7/25/2019
On the side of the triangle , point is selected. In triangle point is the center of the inscribed circle, is the center of excircle wrt side . In the triangle point is the center of the inscribed circle, is the center of excircle wrt side . Prove that the line passing through the midpoints of the segments and is perpendicular to .
geometrymidpointincenterexcenter