In the given figure, triangle ABC is congruent to triangle EDA. If x and y are points lying on AD and EG respectively such that AX/XC = EY/YG = 1 .The value of DC/FY is always
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<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.
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