6
Problems(2)
locus of incenter is a line, starting with non intersecting circles, ext. each
Source: 2009 Oral Moscow Geometry Olympiad grades 8-9 p6
9/19/2020
Fixed two circles and , one of their external tangent and one of their internal tangent . On the line , a point is chosen, and on the line , points and are constructed so that and touch and , respectively, and the triangle contains circles and . Prove that the centers of the circles inscribed in triangles lie on one line.(P. Kozhevnikov)
geometryincentercircles
symmedian wanted, starting with intersecting circles
Source: 2009 Oral Moscow Geometry Olympiad grades 10-11 p6
9/14/2020
To two circles and , intersecting at points and , their common tangent is drawn ( and are tangency points, respectively, point is closer to line than ). Line passing through , intersects and for second time at points and , respectively ( lies between and ). Lines and intersect at point . Prove that is the symmedian of triangle .(Yu. Blinkov)
geometrysymmediancircles