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Angles in Triangle

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January 5, 2007
geometryrhombustrapezoidfloor functionAMCAIMEtrigonometry

Problem Statement

In triangle ABC,ABC, it is given that angles BB and CC are congruent. Points PP and QQ lie on AC‾\overline{AC} and AB‾,\overline{AB}, respectively, so that AP=PQ=QB=BC.AP=PQ=QB=BC. Angle ACBACB is rr times as large as angle APQ,APQ, where rr is a positive real number. Find the greatest integer that does not exceed 1000r.1000r.
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