A very tricky question

Geometry Level 2

In rectangle ABCD, AB = 8 and BC = 20. Let P be a point on AD such that \( \angle BPC = 90^\circ \).

If r1, r2, r3 are the radii of the incircles of triangles AP B, BP C and CP D, what is the value of r1 + r2 + r3?

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