Tangentia Dance

Geometry Level 3

In a 2D world, the circles are organizing a 'Circle Party', where they sing and perform their traditional 'Tagentia Dance'.

In the 'Tangentia Dance' , all the Circles arrange themselves in a circle and hold the largest possible number of different ribbons such that the ribbons are tangents to both of the Circles holding them.

If \( 20 \) Circles are performing this year, how many ribbons are required for the 'Tangentia Dance' ?

Details and assumptions :

  1. The question talks about the maximum number of tangents possible between all the circles.
  2. Every ribbon is connecting only \(2\) Circles.

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