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ABCD is a parallelogram in the given figure, AB is divided at P and CD and Q so that AP:PB=3:2 and CQ:QD=4:1. If PQ meets AC at R, prove that AR= 3/7 AC.
Ans: ΔAPR ∼ ΔCQR (AA)
⇒ AP/CQ = PR/QR = AR/CR
⇒ AP/CQ = AR /CR & AP= 3/5 AB
⇒ 3 AB/5CQ = AR/ CR & CQ= 4/5 CD = 4/5 AB
⇒ AR/CR = 3/4
⇒ CR/AR = 4/3
CR + AR/AR = 4 +1/3
⇒ AC/AR = 7/3
⇒ AR = 3/7 AC
Hence proved
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