4

Part of 2019 China National Olympiad

Problems(1)

Unique rhombus of minimum area tangent to ellipse

Source: China Mathematical Olympiad 2019 Q4

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.

geometryrhombusconicsellipse