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Question
ABCD is a parallelogram. Point P divides AB in the ratio 2:3 and point Q divides DC in the ratio 4:1. Prove that OC is half of OA.
Solution
ABCD is a parallelogram.
AB = DC = a
Point P divides AB in the ratio 2:3
AP = `2/5a`, BP = `3/5a`
Point Q divides DC in the ratio 4:1.
DQ = `4/5a`, CQ = `1/5a`
ΔAPO ∼ ΔCQO ...[AA similarity]
`(AP)/(CQ) = (PO)/(QO) = (AO)/(CO)`
`(AO)/(CO) = (2/5a)/(1/5a) = 2/1`
`\implies` OC = `1/2 OA`
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