Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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Problem A. 449. (March 2008)

A. 449. In the convex quadrilateral ABCD, denote by rA, rB, rC and rD the inradii of triangles BCD, CDA, DAB and ABC, respectively. Prove that the quadrilateral ABCD is cyclic if and only if rA+rC=rB+rD.

Chinese problem

(5 pont)

Deadline expired on April 15, 2008.


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 solutions.

Problems in Mathematics of KöMaL, March 2008