INMO - 2004

Geometry Level pending

Consider a convex quadrilateral \(ABCD\), in which \(K,L,M,N\) are the midpoints of \(AB, BC, CA,\) & \(AD\) respectively. Suppose

\(BD\) bisects \(KM\) at \(Q\);

\(QA = QB = QC = QD\);

\(\frac{LK}{LM} = \frac{CD}{CB}\);

then, find the arithmetic mean of \(\angle A, \angle B\) & \(\angle C\) taken in degrees.

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