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Category: Geometry

P-Q-R-S-are-four-locations-on-the-same-horizontal-plane-Q-is-on-a-bearing-of-041-from-P-and-the-distance-is-40km-S-is-28km-from-R-on-a-bearing-074-R-is-directly-due-north-of-P-and-the-distance-be

Question Number 13738 by chux last updated on 22/May/17 $$\mathrm{P},\mathrm{Q},\mathrm{R},\mathrm{S}\:\mathrm{are}\:\mathrm{four}\:\mathrm{locations}\:\mathrm{on}\:\mathrm{the} \\ $$$$\mathrm{same}\:\mathrm{horizontal}\:\mathrm{plane}.\mathrm{Q}\:\mathrm{is}\:\mathrm{on}\:\mathrm{a}\: \\ $$$$\mathrm{bearing}\:\mathrm{of}\:\mathrm{041}°\:\mathrm{from}\:\mathrm{P}\:\mathrm{and}\:\mathrm{the} \\ $$$$\mathrm{distance}\:\mathrm{is}\:\mathrm{40km}. \\ $$$$\mathrm{S}\:\mathrm{is}\:\mathrm{28km}\:\mathrm{from}\:\mathrm{R}\:\mathrm{on}\:\mathrm{a}\:\mathrm{bearing}\:\mathrm{074}°, \\ $$$$\mathrm{R}\:\mathrm{is}\:\mathrm{directly}\:\mathrm{due}\:\mathrm{north}\:\mathrm{of}\:\mathrm{P}\:\mathrm{and} \\ $$$$\mathrm{the}\:\mathrm{distance}\:\mathrm{between}\:\mathrm{Q}\:\mathrm{and}\:\mathrm{R}\:\mathrm{is} \\ $$$$\mathrm{38km}. \\…

Question-13735

Question Number 13735 by b.e.h.i.8.3.4.1.7@gmail.com last updated on 22/May/17 Commented by b.e.h.i.8.3.4.1.7@gmail.com last updated on 22/May/17 $$\measuredangle{ABC}=\mathrm{90},{S}_{{ABC}} =\mathrm{1},{AB}={BC} \\ $$$$\measuredangle{ABD}=\measuredangle{DBE}=\measuredangle{EBC} \\ $$$${EG}\bot{AB},\:{DF}\bot{BC} \\ $$$$………………………………………………… \\…

Question-79254

Question Number 79254 by mr W last updated on 23/Jan/20 Commented by mr W last updated on 23/Jan/20 $${If}\:{the}\:{side}\:{length}\:{of}\:{the}\:{square}\:{is}\:\mathrm{10}, \\ $$$${find} \\ $$$$\left.\mathrm{1}\right)\:{the}\:{radius}\:{of}\:{the}\:{smallest}\:{circle} \\ $$$$\left.\mathrm{2}\right)\:{the}\:{shaded}\:{area}…

Question-13548

Question Number 13548 by b.e.h.i.8.3.4.1.7@gmail.com last updated on 20/May/17 Commented by b.e.h.i.8.3.4.1.7@gmail.com last updated on 22/May/17 $${in}\:{triangle}\:{ABC}: \\ $$$$\left.\mathrm{1}\right)\measuredangle{ABD}=\measuredangle{DBE}=\measuredangle{EBC} \\ $$$$\left.\mathrm{2}\right){EH}\bot{AB},\:{DG}\bot{BC} \\ $$$$\left.\mathrm{3}\right){S}_{{ABC}} =\mathrm{1} \\…

Question-79026

Question Number 79026 by TawaTawa last updated on 22/Jan/20 Commented by mathmax by abdo last updated on 22/Jan/20 $${we}\:{consider}\:{the}\:{repere}\:\left({D},{D}\overset{\rightarrow} {{C}},{D}\overset{\rightarrow} {{A}}\right)\:\Rightarrow{D}\left(\mathrm{0},\mathrm{0}\right)\:,{C}\left(\mathrm{1},\mathrm{0}\right)\:{A}\left(\mathrm{0},\mathrm{1}\right) \\ $$$$\left(\mathrm{1}=\mathrm{20}{cm}\right)\:\Rightarrow{B}\left(\mathrm{1},\mathrm{1}\right)\:\:{and}\:{F}\left(\frac{\mathrm{1}}{\mathrm{2}},\mathrm{1}\right)\:\:{coordonnate}\:{of}\:{I}? \\ $$$${M}\left({x},{y}\right)\:\in\:\left({CF}\right)\:\Rightarrow{det}\left({C}\overset{\rightarrow}…