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In triangle ABO , angle AOB =90°
AB^2=AO^2+BO^2
AB^2=(1/2AC)^2+(1/2BD)^2....
[AO =1/2AC and BO =1/2 BD]
AB^2=1/4AC^2+1/4BD^2
AB^2=(AC^2+BD^2)/4......
on cross multiplying we get,
4AB^2=AC^2+BD^2
AB^2=AO^2+BO^2
AB^2=(1/2AC)^2+(1/2BD)^2....
[AO =1/2AC and BO =1/2 BD]
AB^2=1/4AC^2+1/4BD^2
AB^2=(AC^2+BD^2)/4......
on cross multiplying we get,
4AB^2=AC^2+BD^2
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