<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