Category: Geometry

Question Number 15917 by mrW1 last updated on 15/Jun/17 Commented by mrW1 last updated on 15/Jun/17 $$\mathrm{E},\mathrm{F},\mathrm{G},\mathrm{H}\mathrm{are}\mathrm{mid}-\mathrm{points}\mathrm{of}\mathrm{the}\mathrm{sides}$$$$\mathrm{of}\mathrm{a}\mathrm{convex}\mathrm{quadrilateral}\mathrm{ABCD}.$$$$\mathrm{L},\mathrm{K}\mathrm{are}\mathrm{mid}-\mathrm{points}\mathrm{of}\mathrm{the}\mathrm{diagonals}.$$$$\mathrm{Prove}\mathrm{that}\mathrm{EG},\mathrm{FH},\mathrm{LK}\mathrm{intersect}\mathrm{at}\mathrm{the}$$$$\mathrm{same}\:\mathrm{point}\:\mathrm{J}\:\:\mathrm{and}\:\mathrm{J}\:\mathrm{is}\:\mathrm{the}\:\mathrm{mid}−\mathrm{point}\:\mathrm{of}\:\:\mathrm{them}.…

Question Number 15904 by mrW1 last updated on 15/Jun/17 Commented by mrW1 last updated on 15/Jun/17 $$\mathrm{A}\mathrm{convex}\mathrm{quadrilateral}\mathrm{ABCD}\mathrm{is}$$$$\mathrm{divided}\mathrm{into}4\mathrm{triangle}\mathrm{by}\mathrm{its}\mathrm{two}$$$$\mathrm{diagonals}.\mathrm{The}\mathrm{centroids}\mathrm{of}\mathrm{these}$$$$\mathrm{triangles}\mathrm{form}\mathrm{a}\mathrm{new}\mathrm{quadrilaterial}.$$$$\mathrm{Find}\:\mathrm{out}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{the}\:\mathrm{new}\:\mathrm{quadri}−…

Question Number 81322 by ajfour last updated on 11/Feb/20 Commented by ajfour last updated on 11/Feb/20 $$Findradiusofquatercircle$$$$intermsofa,b,c.$$ Answered by mr W…

Question Number 15782 by mrW1 last updated on 13/Jun/17 Commented by mrW1 last updated on 13/Jun/17 $$\mathrm{E}\mathrm{and}\mathrm{F}\mathrm{are}\mathrm{midpoint}\mathrm{of}\mathrm{AB}\mathrm{and}\mathrm{CD}.$$$$\mathrm{Prove}\mathrm{that}$$$$\mathrm{area}\mathrm{yellow}=\mathrm{area}\mathrm{green}$$ Answered by…

Question Number 81289 by 37996827 last updated on 11/Feb/20 $$discussthesymmetryofthefollowingcurves$$$$squareofx+squareofy=1$$ Commented by mr W last updated on 11/Feb/20 $$itisacirclewithradiusof1andcenterat$$$${theoriginwhichissymmetricaboutevery}…