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5. * In a parallogram ABCD, P divides AB in the ratio 2 : 5 and Q divides DC in the ratio 3 : 2. If AC and PQ intersect at R, find the ratios AR : RC and PR : RQ

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Answer

AR: RC = 1 : 1 and PR : RQ = 1 : 1

Explanation:

Using figure 1 as shown below.


In\triangle ARP and \triangle QRC.


\angle ARP =\angle QRC (vertically\ opposite\ angles)


\angle PAR =\angle QCR \ (\because AB \parallel CD)


\therefore \triangle ARP\sim \triangle QRC
(by AA similarity)


\therefore(AP)/(AR) =(QC)/(RC)


(2x)/(AR) =(2x)/(RC)


AR: RC = 1: 1

In the similar way,


(QC)/(RQ) =(AP)/(PR)


(PR)/(RQ) = (AP)/(QC) =(2x)/(2x)


Therefore, PR: RQ = 1: 1

5. * In a parallogram ABCD, P divides AB in the ratio 2 : 5 and Q divides DC in the-example-1
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