Question

In the given figure, ΔABC congruent triangle EDA. If X and Y are point lying on AD and EG respectively such that AX/XC = EY/YG =1 The value of DX/FY is always

Answer 1

<EGF = <DGC = 90° - <C

<E = <A = 90° - <C

<E = <EGF = >EF = FG

FY is the median in the triangle FEG

FY is the perpendicular to ED

FE // AC (this is the equation 1)

Join BX

BX is the median of triangle ABC

BX = 1/2 AC = XC

<XBC = <C = DAE

ABFX is cyclic quadrilateral

<<AXF = 180° - <ABF = 90°

FX is perpendicular to AC (this equation will be 2)

so from equation 1 and 2

DXFY is a rectangle  = DX = FY

DX/FY = 1

If there is any confusion please leave a comment below.