Menu Close

Category: Geometry

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 ConsidertheareasofthefourtrianglesobtainedbydrawingthediagonalsACandBDofatrapeziumABCD.Theproductoftheseareas,takentwoattime,arecomputed.Ifamongthesixproductssoobtained,twoproductsare1296and576,determinethesquare$$\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 LetPbeaninteriorpointofatriangleABCwhosesidelengthsare26,65,78.ThelinethroughPparalleltoBCmeetsABinKandACinL.ThelinethroughPparalleltoCAmeetsBCinMandBAinN.ThelinethroughPparalleltoABmeetsCAinSandCBinT.IfKL,MN,$${ST},\:\mathrm{are}\:\mathrm{of}\:\mathrm{equal}\:\mathrm{lengths},\:\mathrm{find}\:\mathrm{this} \