Let P(r) denote the circle with point P as its center and r as its radius.

Let AB be a chord of O(r) and let the perpendicular bisector of AB intersect O(r)
at points C and D and chord AB at point M such that M lies between O and C.

Let O₁(r₁), O₂(r₂), and O₃(r₃) lie within circular segment ADB and be tangent to AB.

Let O₁(r₁) and O₃(r₃) be internally tangent to O(r) and externally tangent to O₂(r₂), but not intersect each other.

If r₂ = |MC|/2, then prove that r = r₁ + r₂ + r₃

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