Question and Answers Forum

All Questions      Topic List

Geometry Questions

Previous in All Question      Next in All Question      

Previous in Geometry      Next in Geometry      

Question Number 16946 by Tinkutara last updated on 28/Jun/17

Consider the quadrilateral ABCD.  The points M, N, P and Q are the  midpoints of the sides AB, BC, CD  and DA.  Let X = AP ∩ BQ, Y = BQ ∩ CM,  Q = CM ∩ DN and T= DN ∩ AP.  Prove that [XYZT] = [AQX] + [BMY]  + [CNZ] + [DPT].

$$\mathrm{Consider}\:\mathrm{the}\:\mathrm{quadrilateral}\:{ABCD}. \\ $$$$\mathrm{The}\:\mathrm{points}\:{M},\:{N},\:{P}\:\mathrm{and}\:{Q}\:\mathrm{are}\:\mathrm{the} \\ $$$$\mathrm{midpoints}\:\mathrm{of}\:\mathrm{the}\:\mathrm{sides}\:{AB},\:{BC},\:{CD} \\ $$$$\mathrm{and}\:{DA}. \\ $$$$\mathrm{Let}\:{X}\:=\:{AP}\:\cap\:{BQ},\:{Y}\:=\:{BQ}\:\cap\:{CM}, \\ $$$${Q}\:=\:{CM}\:\cap\:{DN}\:\mathrm{and}\:{T}=\:{DN}\:\cap\:{AP}. \\ $$$$\mathrm{Prove}\:\mathrm{that}\:\left[{XYZT}\right]\:=\:\left[{AQX}\right]\:+\:\left[{BMY}\right] \\ $$$$+\:\left[{CNZ}\right]\:+\:\left[{DPT}\right]. \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com