In Fig. \( \quad \mathrm{ABCD} \) is a parallelogram and \( \mathrm{BC} \) is produced to a poin...

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In Fig. \( \quad \mathrm{ABCD} \) is a parallelogram and \( \mathrm{BC} \) is produced to a point \( \mathrm{Q} \) such that \( \mathrm{AD}=\mathrm{CQ} \). If \( \mathrm{AQ} \) intersect \( \mathrm{DC} \) at \( \mathrm{P} \), show that \( \operatorname{ar}(\mathrm{BPC})=\operatorname{ar}(\mathrm{DPQ}) \).
[Hint : Join AC.]
IV
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