Advanced Geometric Problem & Solution (Twice a week update) Now 4565 problems posted.
<Tri-2024-2134>, hint
Consider complex coordinate .
Let B(0,0) BC=c, BA=a, M be the midpoint of AB, <PBA =w. BP/BM=k.
z=k( cosw + isinw)
BP=a/2 z, BQ=c/2 z hence PQ=z/2(a-c).
Similarly BR=1/2(a-c) z+c Hence CR=BR-BC=1/2(a-c)z+c-c=z/2(a-c)=PQ
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