Find the centre of circle opposite to A

Geometry Level 3

Find the coordinate of the centre of the circle opposite to vertex A which touch the sides of the triangle the co-ordinates of whose angular points are the points \(A =( 6 , 0 ) , B =( 0 , 6 ) ,C =( 7 , 7 )\).

The answer would be in the form of \( ( \frac ab , \frac cd ) \) with \( \text{gcd}(a,b)=\text{gcd}(c,d) = 1 \). What is the value of \(a+b+c+d+1\)?

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