How can one show that (DI) , (JB) and (AC) concurrents on G?

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ABCD is a square , We add outside it two equilateral triangles ADJ and ABI How can I show that (DI) and (BJ) and (AC) occur in the same point ? Here can we demontrate that saying that IGB and JGD are isometric on The line (AC) ?! What about the circle ?! I added somthing ... G is the point of masse of IJC ??! Can someone give me a suggestion ?! I don't want the answee I have to work my mind ... THANKS