Wikipedia states the problem as follows: ""The Bertrand paradox goes as follows: Consider an equilateral triangle inscribed in a circle. Suppose a chord of the circle is chosen at random. What is the probability that the chord is longer than a side of the triangle?""
solution being 1/2 seems to be the only solution as parallel chords have 1/2 probability to be longer than a side of the triangle.
I don't understand other solutions. Am I missing something?
To be more specific as requested, other solutions are based on circle arc and area (both are 2-dimensional).
The question is: why the use of 2-dimensional structures is appropriate/correct when solving Bertrand paradox?
