Unique rhombus of minimum area tangent to ellipse
Source: China Mathematical Olympiad 2019 Q4
November 15, 2018
geometryrhombusconicsellipse
Problem Statement
Given an ellipse that is not a circle.
(1) Prove that the rhombus tangent to the ellipse at all four of its sides with minimum area is unique.
(2) Construct this rhombus using a compass and a straight edge.