Prove that ar= 3/7 ac of parallelogram , Mathematics

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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.

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Ans:    ΔAPR ∼ ΔCQR (AA)

⇒  AP/CQ = PR/QR = AR/CR

⇒  AP/CQ = AR /CR   & AP= 3/5 AB

⇒ 3 AB/5C = 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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