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In rectangle ABCDABCDABCD, AB‾=8\overline{AB}=8AB=8 and BC‾=20\overline{BC} = 20BC=20. Let PPP be a point on AD‾\overline{AD}AD such that ∠BPC=90°\angle BPC = 90\degree∠BPC=90°.
If r1,r2,r3r_1, r_2, r_3r1,r2,r3 are the radii of the in-circles of triangles △APB,△BPC\triangle {APB}, \triangle {BPC}△APB,△BPC and △CPD\triangle CPD△CPD.
What is the value of r1+r2+r3r_1 + r_2 + r_3r1+r2+r3?
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