Bulgaria 7
Source: IMO LongList 1959-1966 Problem 33
September 2, 2004
geometrytangent circlesInequalitygeometric inequalityIMO ShortlistIMO Longlist
Problem Statement
Given two internally tangent circles; in the bigger one we inscribe an equilateral triangle. From each of the vertices of this triangle, we draw a tangent to the smaller circle. Prove that the length of one of these tangents equals the sum of the lengths of the two other tangents.