It is given that BO = OD
From the figure we know that AO is the median of △ ABD
So we get
Area of △ AOD = Area of △ AOB ……. (1)
We know that OC is the median of △ CBD
So we get
Area of △ DOC = Area of △ BOC ……. (2)
By adding both the equations
Area of △ AOD + Area of △ DOC = Area of △ AOB + Area of △ BOC
So we get
Area of △ ADC = Area of △ ABC
Therefore, it is proved that ar (△ ABC) = ar (△ ADC).