Question

In the given figure, ∆ABC congruent to ∆EDA. If X and Y are the points lying on AD and EG respectively such that AX/XC = EY/YG= 1. Then value of DX/FY is always ?
Options are
1) Greater than 1
2) Equal to 1
3) Less than 1
4) Equal to 3/2

Answer 1

2 hope it will help....

Answer 2

<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.