Question Number 148132 by Jonathanwaweh last updated on 25/Jul/21 Answered by Olaf_Thorendsen last updated on 25/Jul/21 $$\mathrm{1}. \\ $$$$\mathrm{ABCD}\:\mathrm{est}\:\mathrm{un}\:\mathrm{rectangle}\:\mathrm{et}\:\mathrm{possede} \\ $$$$\mathrm{donc}\:\mathrm{4}\:\mathrm{angles}\:\mathrm{droits}\:\mathrm{que}\:\mathrm{les} \\ $$$$\mathrm{bissectrices}\:\mathrm{divisent}\:\mathrm{a}\:\mathrm{45}°. \\ $$$$\mathrm{On}\:\mathrm{a}\:\mathrm{donc}\::…
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Question Number 82528 by TawaTawa last updated on 22/Feb/20 Commented by TawaTawa last updated on 22/Feb/20 $$\mathrm{Please}\:\mathrm{help}. \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 16980 by mrW1 last updated on 29/Jun/17 $$\mathrm{To}\:\mathrm{Q16066}: \\ $$$$\mathrm{I}\:\mathrm{have}\:\mathrm{posted}\:\mathrm{my}\:\mathrm{solution}\:\mathrm{there}. \\ $$$$\mathrm{Those}\:\mathrm{who}\:\mathrm{are}\:\mathrm{intetested}\:\mathrm{in}\:\mathrm{this}\:\mathrm{interesting} \\ $$$$\mathrm{question}\:\mathrm{please}\:\mathrm{have}\:\mathrm{a}\:\mathrm{critical}\:\mathrm{view}\:\mathrm{at} \\ $$$$\mathrm{it}.\:\mathrm{Maybe}\:\mathrm{there}\:\mathrm{are}\:\mathrm{alternative}\:\mathrm{solutions} \\ $$$$\mathrm{which}\:\mathrm{are}\:\mathrm{easier}\:\mathrm{and}\:\mathrm{more}\:\mathrm{direct}\:\mathrm{and} \\ $$$$\mathrm{straight}\:\mathrm{on}. \\ $$ Commented…
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Question Number 16958 by Tinkutara last updated on 28/Jun/17 $$\mathrm{Let}\:{ABCD}\:\mathrm{be}\:\mathrm{a}\:\mathrm{quadrilateral}\:\mathrm{with}\:\mathrm{an} \\ $$$$\mathrm{inscribed}\:\mathrm{circle}.\:\mathrm{Prove}\:\mathrm{that}\:\mathrm{the}\:\mathrm{circles} \\ $$$$\mathrm{inscribed}\:\mathrm{in}\:\mathrm{triangles}\:{ABC}\:\mathrm{and}\:{ADC} \\ $$$$\mathrm{are}\:\mathrm{tangent}\:\mathrm{to}\:\mathrm{each}\:\mathrm{other}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 16951 by Tinkutara last updated on 28/Jun/17 $$\mathrm{Let}\:{M}\:\mathrm{be}\:\mathrm{a}\:\mathrm{point}\:\mathrm{in}\:\mathrm{interior}\:\mathrm{of}\:\Delta{ABC}. \\ $$$$\mathrm{Three}\:\mathrm{lines}\:\mathrm{are}\:\mathrm{drawn}\:\mathrm{through}\:{M}, \\ $$$$\mathrm{parallel}\:\mathrm{to}\:\mathrm{triangle}'\mathrm{s}\:\mathrm{sides},\:\mathrm{thereby} \\ $$$$\mathrm{producing}\:\mathrm{three}\:\mathrm{trapezoids}.\:\mathrm{Suppose}\:\mathrm{a} \\ $$$$\mathrm{diagonal}\:\mathrm{is}\:\mathrm{drawn}\:\mathrm{in}\:\mathrm{each}\:\mathrm{trapezoid}\:\mathrm{in} \\ $$$$\mathrm{such}\:\mathrm{a}\:\mathrm{way}\:\mathrm{that}\:\mathrm{the}\:\mathrm{diagonals}\:\mathrm{have}\:\mathrm{no} \\ $$$$\mathrm{common}\:\mathrm{endpoints}.\:\mathrm{These}\:\mathrm{three} \\ $$$$\mathrm{diagonals}\:\mathrm{divide}\:{ABC}\:\mathrm{into}\:\mathrm{seven} \\…
Question Number 16947 by Tinkutara last updated on 28/Jun/17 $$\mathrm{Through}\:\mathrm{the}\:\mathrm{vertices}\:\mathrm{of}\:\mathrm{the}\:\mathrm{smaller} \\ $$$$\mathrm{base}\:{AB}\:\mathrm{of}\:\mathrm{the}\:\mathrm{trapezoid}\:{ABCD}\:\mathrm{two} \\ $$$$\mathrm{parallel}\:\mathrm{lines}\:\mathrm{are}\:\mathrm{drawn},\:\mathrm{intersecting} \\ $$$$\mathrm{the}\:\mathrm{segment}\:{CD}.\:\mathrm{These}\:\mathrm{lines}\:\mathrm{and}\:\mathrm{the} \\ $$$$\mathrm{trapezoid}'\mathrm{s}\:\mathrm{diagonals}\:\mathrm{divide}\:\mathrm{it}\:\mathrm{into} \\ $$$$\mathrm{seven}\:\mathrm{triangles}\:\mathrm{and}\:\mathrm{a}\:\mathrm{pentagon}.\:\mathrm{Show} \\ $$$$\mathrm{that}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{the}\:\mathrm{pentagon}\:\mathrm{equals} \\ $$$$\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{areas}\:\mathrm{of}\:\mathrm{the}\:\mathrm{three} \\…
Question Number 16946 by Tinkutara last updated on 28/Jun/17 $$\mathrm{Consider}\:\mathrm{the}\:\mathrm{quadrilateral}\:{ABCD}. \\ $$$$\mathrm{The}\:\mathrm{points}\:{M},\:{N},\:{P}\:\mathrm{and}\:{Q}\:\mathrm{are}\:\mathrm{the} \\ $$$$\mathrm{midpoints}\:\mathrm{of}\:\mathrm{the}\:\mathrm{sides}\:{AB},\:{BC},\:{CD} \\ $$$$\mathrm{and}\:{DA}. \\ $$$$\mathrm{Let}\:{X}\:=\:{AP}\:\cap\:{BQ},\:{Y}\:=\:{BQ}\:\cap\:{CM}, \\ $$$${Q}\:=\:{CM}\:\cap\:{DN}\:\mathrm{and}\:{T}=\:{DN}\:\cap\:{AP}. \\ $$$$\mathrm{Prove}\:\mathrm{that}\:\left[{XYZT}\right]\:=\:\left[{AQX}\right]\:+\:\left[{BMY}\right] \\ $$$$+\:\left[{CNZ}\right]\:+\:\left[{DPT}\right]. \\…