Problem A. 449. (March 2008)

A. 449. In the convex quadrilateral ABCD, denote by r_A, r_B, r_C and r_D the inradii of triangles BCD, CDA, DAB and ABC, respectively. Prove that the quadrilateral ABCD is cyclic if and only if r_A+r_C=r_B+r_D.

Chinese problem

(5 pont)

Deadline expired on April 15, 2008.

Statistics:

8 students sent a solution.
5 points:	Lovász László Miklós, Tossenberger Anna, Wolosz János.
4 points:	Huszár Kristóf.
3 points:	1 student.
0 point:	1 student.
Unfair, not evaluated:	2 solutionss.

Problems in Mathematics of KöMaL, March 2008