# 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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