Ruler-&-compass construction of triangle with minimum area
Source: XII Rioplatense Mathematical Olympaid (2003), Level 3
August 9, 2011
geometryinequalitiesinradiusgeometry unsolved
Problem Statement
Inside right angle , where is the vertex, is a semicircle whose center lies on and that is tangent to at the point . Describe a ruler-and-compass construction for the tangent to such that the triangle enclosed by the tangent and angle has minimum area.