The vertices of a triangle are A(1, 1), B(0, 0) and C(2, 0). The angular bisectors of the triangle meet at P. What are the coordinates of P?

Incentre = (a·A + b·B + c·C)/(a+b+c) where a=BC, b=CA, c=AB. a = BC = 2, b = CA = √((2-1)²+1) = √2, c = AB = √2. Incentre x = (2·1 + √2·0 + √2·2)/(2+2√2) = (2 + 2√2)/(2+2√2) = 1. Incentre y = (2·1 + √2·0 + √2·0)/(2+2√2) = 2/(2+2√2) = 1/(1+√2) = √2 - 1. So P = (1, √2-1).