



 
Bob, If the inscribed circle with center O touches ABCD at W (on AB), X(on BC), Y(on CD) and Z (on DA), then triangles OAW, OAZ are congruent (why?) as are three other pairs. [Draw and label the diagram] So AW = AZ [and three other equalities  find them!] Deduce from this that AB + CD = BC + AD for any quadrilateral with an inscribed circle. (Less obviously, this is ifandonlyif.) Solve your problem. Good hunting!  


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