Question

等腰直角三角形ABC中,角C等于90度,AC=BC,点P

Answer 1

△ABC△BFP△AEP都为等腰直角三角形,则PE=AE,AB^2=2AC^2,BP^2=2CE,BP=√2CE,又CE=PF

Rt△CEP中

CP^2=CE^2+PE^2

=CE^2+AE^2

=CE^2+(AC+CE)^2

=2CE^2+AC^2+2AC▪CE

=BP^2+1/2AB^2+AB▪BP

=BP^2+1/2(AP-BP)^2+(AP-BP)▪BP

=1/2AP^2+1/2BP^2