Question

in triangle abc ad perpendicular to BC if ad square equals to BD into DX prove that angle BAC equals to 90 degrees

Answer 1

BD^2+AD^2=AB^2 (1 eq)

DC^2++AD^2=AC^2 (2 eq)

On adding eq.(1) & (3)

BD^2+DC^2+2AD^2=AB^2+AC^2

Put AD^2=BD.DC (given)

BD^2+DC^2+2BD.DC=AB^2+AC^2

(BD+DC)^2=AB^+AC^2 , put BD+DC=BC

BC^2=AB^2+AC^2 , therefore in triangle ABC

BC is hypotenues and angle BAC=90° , Proved.