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It is hard to interpret what you are asking.
Do you mean 'radial' instead of 'horizontal'?
Are you referring only to a horizontal circle? Because in a non-horizontal circle, 'horizontal resultant force' doesn't mean much.
Are you referring only to uniform motion, or are you considering the possibility of non-uniform motion?
Centripetal force is NEVER directed outwards. It is the force that makes the object travel in a circle.
It is always directed towards the centre (which is basically what the word 'centripetal' means), and for uniform circular motion that is the only net force.
You should be calling the direction radial, NOT horizontal. In a horizontal circle, 'horizontal' could mean anything.
For non-uniform motion, there is also a tangential component. The vector sum of the radial and tangential components won't point at the centre, but it will never point outwards.
Other than that, I can't offer any more help without a specific question from you.
Question 4b of 2009: the answers state the the resultant radial force is outwards rather than inwards.
The solutions stated mrw2= TsinA - NcosA rather than NcosA - TsinA.