Open problem

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It is given convex quadrilateral and a circle k with radii r inscribed in ABCD.
Incircles radii of the triangles ABC, BCD, CDA, DAB are r_1, r_2, r_3, r_4.
a) Is it possible to find a dependency between r_1, r_2, r_3, r_4?
b) Is it possible express r in therms of r_1, r_2, r_3, r_4?
c) If a) and/or b) is true what is the dependency?

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Is the problem boring or it is too hard?

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I saw two Sangaku problems and a problem from Wu Wei Zao from 1999-2000 it is the reason I'm asking such questions. Probably the problem is not easy at all but for excellent mathematician it not impossible to solve.
What are your opinions and ideas?

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http://forumgeom.fau.edu/FG2009volume9/FG200910.pdf
Can this one be useful?

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http://www.artofproblemsolving.com/Foru ... drilateral
Or that?!

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