Menu Close

Category: Geometry

Question-86907

Question Number 86907 by TawaTawa1 last updated on 01/Apr/20 Commented by mr W last updated on 01/Apr/20 $${question}\:{is}\:{wrong}\:!? \\ $$$${there}\:{are}\:{infinite}\:{possibilities}\:{for} \\ $$$${PQRS}. \\ $$$$\frac{\left[{PQRS}\right]}{\Delta{ABC}}\neq{constant},\:{but}\:{min}.=\frac{\mathrm{2}}{\mathrm{5}} \\…

What-do-you-guys-think-of-creating-a-Telegram-group-to-discuss-theory-and-more-descriptive-questions-

Question Number 21310 by dioph last updated on 20/Sep/17 $$\mathrm{What}\:\mathrm{do}\:\mathrm{you}\:\mathrm{guys}\:\mathrm{think}\:\mathrm{of} \\ $$$$\mathrm{creating}\:\mathrm{a}\:\mathrm{Telegram}\:\mathrm{group}\:\mathrm{to} \\ $$$$\mathrm{discuss}\:\mathrm{theory}\:\mathrm{and}\:\mathrm{more}\:\mathrm{descriptive} \\ $$$$\mathrm{questions}? \\ $$ Commented by imistakedn last updated on 20/Sep/17…

Consider-the-areas-of-the-four-triangles-obtained-by-drawing-the-diagonals-AC-and-BD-of-a-trapezium-ABCD-The-product-of-these-areas-taken-two-at-time-are-computed-If-among-the-six-products-so-obta

Question Number 21231 by Tinkutara last updated on 16/Sep/17 $$\mathrm{Consider}\:\mathrm{the}\:\mathrm{areas}\:\mathrm{of}\:\mathrm{the}\:\mathrm{four}\:\mathrm{triangles} \\ $$$$\mathrm{obtained}\:\mathrm{by}\:\mathrm{drawing}\:\mathrm{the}\:\mathrm{diagonals}\:{AC} \\ $$$$\mathrm{and}\:{BD}\:\mathrm{of}\:\mathrm{a}\:\mathrm{trapezium}\:{ABCD}.\:\mathrm{The} \\ $$$$\mathrm{product}\:\mathrm{of}\:\mathrm{these}\:\mathrm{areas},\:\mathrm{taken}\:\mathrm{two}\:\mathrm{at} \\ $$$$\mathrm{time},\:\mathrm{are}\:\mathrm{computed}.\:\mathrm{If}\:\mathrm{among}\:\mathrm{the}\:\mathrm{six} \\ $$$$\mathrm{products}\:\mathrm{so}\:\mathrm{obtained},\:\mathrm{two}\:\mathrm{products}\:\mathrm{are} \\ $$$$\mathrm{1296}\:\mathrm{and}\:\mathrm{576},\:\mathrm{determine}\:\mathrm{the}\:\mathrm{square} \\ $$$$\mathrm{root}\:\mathrm{of}\:\mathrm{the}\:\mathrm{maximum}\:\mathrm{possible}\:\mathrm{area}\:\mathrm{of} \\…

Let-P-be-an-interior-point-of-a-triangle-ABC-whose-sidelengths-are-26-65-78-The-line-through-P-parallel-to-BC-meets-AB-in-K-and-AC-in-L-The-line-through-P-parallel-to-CA-meets-BC-in-M-and-BA-in-N-

Question Number 21228 by Tinkutara last updated on 16/Sep/17 $$\mathrm{Let}\:{P}\:\mathrm{be}\:\mathrm{an}\:\mathrm{interior}\:\mathrm{point}\:\mathrm{of}\:\mathrm{a}\:\mathrm{triangle} \\ $$$${ABC}\:\mathrm{whose}\:\mathrm{sidelengths}\:\mathrm{are}\:\mathrm{26},\:\mathrm{65},\:\mathrm{78}. \\ $$$$\mathrm{The}\:\mathrm{line}\:\mathrm{through}\:{P}\:\mathrm{parallel}\:\mathrm{to}\:{BC}\:\mathrm{meets} \\ $$$${AB}\:\mathrm{in}\:{K}\:\mathrm{and}\:{AC}\:\mathrm{in}\:{L}.\:\mathrm{The}\:\mathrm{line}\:\mathrm{through} \\ $$$${P}\:\mathrm{parallel}\:\mathrm{to}\:{CA}\:\mathrm{meets}\:{BC}\:\mathrm{in}\:{M}\:\mathrm{and}\:{BA} \\ $$$$\mathrm{in}\:{N}.\:\mathrm{The}\:\mathrm{line}\:\mathrm{through}\:{P}\:\mathrm{parallel}\:\mathrm{to}\:{AB} \\ $$$$\mathrm{meets}\:{CA}\:\mathrm{in}\:{S}\:\mathrm{and}\:{CB}\:\mathrm{in}\:{T}.\:\mathrm{If}\:{KL},\:{MN}, \\ $$$${ST},\:\mathrm{are}\:\mathrm{of}\:\mathrm{equal}\:\mathrm{lengths},\:\mathrm{find}\:\mathrm{this} \\…