# Hosam Hajjir vs Maria Kozlowska

**Geometry**Level 3

Twin ellipses have semiminor axes of length 1 and semimajor axes of length 2. In one ellipse, the semiminor axis is horizontal; in the other, the semimajor axis is horizontal. The twin ellipses are tangent and the horizontal axes (semiminor for one, semimajor for the other) lie on the same line. The twin ellipses lie on opposite sides of their common tangent line.

What is the minimum diameter of the circle that encloses both ellipses?

Provide your answer to 3 decimals places.