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GeometryQuestion and Answers: Page 78
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$$\mathrm{A}\:\mathrm{circle}\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} −\mathrm{2x}−\mathrm{4y}−\mathrm{5}=\mathrm{0}\:\mathrm{with}\:\mathrm{centr} \\ $$$$\mathrm{0}\:\mathrm{is}\:\mathrm{cut}\:\mathrm{by}\:\mathrm{a}\:\mathrm{line}\:\mathrm{y}=\mathrm{2x}+\mathrm{5}\:\mathrm{at}\:\mathrm{points}\:\mathrm{P}\:\mathrm{and}\:\mathrm{Q}. \\ $$$$\mathrm{Show}\:\mathrm{that}\:\mathrm{QO}\:\mathrm{is}\:\mathrm{perpendicular}\:\mathrm{to}\:\mathrm{PO}. \\ $$
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$$\mathrm{ABCD}\:\:\mathrm{is}\:\mathrm{a}\:\mathrm{square},\:\mathrm{AC}\:\mathrm{is}\:\mathrm{a}\:\mathrm{diagonal}.\:\mathrm{If}\:\:\mathrm{the}\:\mathrm{coordinate}\:\mathrm{of}\:\:\mathrm{A},\:\mathrm{C} \\ $$$$\mathrm{are}\:\:\left(−\:\mathrm{5},\:\mathrm{8}\right)\:\mathrm{and}\:\left(\mathrm{7},\:−\:\mathrm{4}\right)\:.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{coordinate}\:\mathrm{of}\:\:\mathrm{B}\:\mathrm{and}\:\mathrm{D}. \\ $$
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$$\:{A}\:{regular}\:{polygon}\:{of}\:\left(\mathrm{2}{k}+\mathrm{1}\right)\:{sides} \\ $$$${has}\:\mathrm{140}\:{as}\:{the}\:{size}\:{of}\:{each}\:{interior} \\ $$$${angle}.{Find}\:{k} \\ $$
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