Interesting problem of a triangle (equal chords)
Source: 10th Iberoamerican 1995 pr. B2
March 30, 2004
geometrytrapezoidtrigonometrysimilar triangles
Problem Statement
The incircle of a triangle touches the sides , , at the points , , respectively. Let the line intersect this incircle of triangle at a point (apart from ). Assume that this point is the midpoint of the segment , this means, . Let the line meet the incircle of triangle at a point (apart from ), and let the line meet the incircle of triangle at a point (apart from ). Show that .