If A(0,0),B(1,0) and C(12,32) are vertices of a triangle, then the centre of the circle for which the lines AB,BC and CA re tangents is

AB=AC=BC=1So, triangle is an equilateral.Thus, incentre coincoide with centroid.Centre of the circle touching all the three sides of triangle is incentre.Therefore, incentre is (0+1+123,0+0+323)≡(12,123)