4 Circles of Pi Day

Geometry Level 3

Two circles \(O_1 , O_2\) are tangent to each other at point \(A\) and has a common tangent \(L_1\) at points \(B , C\). Another line \(L_2\) is parellel to line \(L_1\) and tangent to circle \(O_1\). If \(O_1\) has a radius of 9, \(O_2\) has a radius of 4, \(O_3\) is tangent to \(O_1 , O_2\) and \(L_1\), \(O_4\) is tangent to \(O_1 , O_2\) and \(L_2\), find the geometric mean of the radiuses of the 4 circles.

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