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In a rectangle ABCD, AB=8 and BC=20. Let...

In a rectangle ABCD, AB=8 and BC=20. Let P be a point on AD such that `/_BPC=90^@` If `r_1,r_2,r_3` are the radii of the incircles of triangles APB, BPC and CPD. What is the value of `r_1+r_2+r_3?`

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