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OCR chemistry a

can someone please spot my mistake? I am struggling to see why my argument is false.

So Kc and Kp tell you about the position of equilibrium, i.e wether or not position of equilibrium lies on reactants side or products side.
Shift in equilibrium is determined by rate constant k
Therefore position of equilibrium is determined by rate constant k
Catalyst speeds up rate of reaction and therefore will increase k
so catalyst should therefore affect k and hence Kc and Kc.
however the book says it doesn't so what went wrong?

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