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Let DF and BC (Extended) meet at point Q. FB:AB=1:7, FB:CD=1:8. AE:ED=1:3, AD:ED=4:3.
Between ΔDQC and ΔFQB, ∠Q is common and ∠BFQ=∠CDQ as AB||CD and QD is bisector. So, ΔDQC~ΔFQB.
Then, FB:CD=QB:QC=1:8
∠QFB=∠AFD, AD||BC||QC, ∠ADF=∠FQB, ΔAFD~ΔBFQ. QB:AD=BF:AF=1:7.
QB/AD × AD/ED= 1/7 × 4/3
or, QB/ED = 4/21
Again, AD:ED=BC:ED=4:3
So, QB/ED + BC/ED = 4/21 + 4/3
or, (QB+BC)/ED = (4+4×7)/21
or, QC/ED = 32/21,
We know, ΔQPC~EPD as AD||BC||QC||ED.
So, CP:PE = QC:ED = 32/21.