because it determines whether the circle is big or small depending on the length of the diameter. Remember that the diameter is not only just a line, it is a line that defines the length from one edge to the other of a circle, so if that distance is smaller, the circle becomes smaller. Lemme explain with an example, if you have a pie and you cut it into slices from the middle and then you take a slice, the length is the radius, all the slices have the same length, so if the slice gets smaller and all slices are equal, then the pie itself reduces in size. The same is true if you grab two slices which make up the diameter and you reduce the length of them, then the pie will inevitably reduce in size.
Idk who asked first, but the ratio was probably used without even knowing the formula in the first place through a rudimentary form of a compass. The Egyptians for instance, used sticks and tense rope to make a compass and thus make circles, the length of the rope functioning as a radius.
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