Creation of this resource was inspired by a [url=http://gogeometry.com/geometry/p700_equilateral_triangle_circle_inscribed_metric_relations_plane_geometry.htm]problem[/url] posted by [url=https://twitter.com/gogeometry]Antonio Gutierrez[/url] (GoGeometry). [br][br]What is the exact value of the ratio of the [b]black segment (side of the [color=#bf9000]larger equilateral triangle[/color]) [/b]to the [b][color=#9900ff]purple segment (side of the [/color][color=#38761d]smaller equilateral triangle)[/color][/b]? [br][br][b][color=#1e84cc]How can we formally prove what is dynamically illustrated here? [/color][/b]