A Pre-RMO question! -24

In rectangle ABCDABCD, AB=8\overline{AB}=8 and BC=20\overline{BC} = 20. Let PP be a point on AD\overline{AD} such that BPC=90°\angle BPC = 90\degree.

If r1,r2,r3r_1, r_2, r_3 are the radii of the in-circles of triangles APB,BPC\triangle {APB}, \triangle {BPC} and CPD\triangle CPD.

What is the value of r1+r2+r3r_1 + r_2 + r_3?

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