Question

In an equatateral triangle ABC, BE is
perpendicular to side CA. Prove that :
AB2 + BC2 + CA2 = 4BE2​

Answer 1

Answer:

PROVED

Step-by-step explanation:

The perpendicular drawn to the equilateral triangle will be the mid point of the side

    so  AE = 1/2 AC

RHS

 =  4 BE^2

  SINCE ABE is right angles triangle AB^2 = BE^2 + AE^2

                                                            BE^2 = AB^2 -  AE^2

       4 BE^2 = 4 ( AB^2 -  AE^2 )

                   = 4AB^2 -  4AE^2

                    = AB^2 + BC^2 + AC ^2 + AC ^2 - 4 ( 1/2 AC )^2

                    =  AB^2 + BC^2 + AC ^2 + AC ^2 -  AC ^2

                    =  AB^2 + BC^2 + AC ^2