Googly Eyed Triangle

Geometry Level 4

Point DD is on side BCBC of ABC.\triangle ABC. The incircle ω1\omega _1 of ABD\triangle ABD is tangent to BCBC at XX and to ADAD at Y.Y. The incircle ω2\omega _2 of ADC\triangle ADC is tangent to BCBC at ZZ and to ADAD at Y.Y. If the radius of ω1\omega _1 is 2,2, and the radius of ω2\omega _2 is 1,1, find the value of XY2+YZ2XY^2 + YZ^2 to the nearest tenth.

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