In a circumference Γ a chord PQ is considered such that the segment that joins the midpoint of the smallest arc PQ and the midpoint of the segment PQ measures 1. Let Γ1,Γ2 and Γ3 be three tangent circumferences to the chord PQ that are in the same half plane than the center of Γ with respect to the line PQ. Furthermore, Γ1 and Γ3 are internally tangent to Γ and externally tangent toΓ2, and the centers of Γ1 and Γ3 are on different halfplanes with respect to the line determined by the centers of Γ and Γ2.
If the sum of the radii of Γ1,Γ2 and Γ3 is equal to the radius of Γ, calculate the radius of Γ2. circlesgeometrytangent circlesradiiradius