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?

Explanation

The intersection of angular bisectors is the incenter. The side lengths are a=BC=2, b=AC=\sqrt{1^2+(-1)^2}=\sqrt{2}, and c=AB=\sqrt{1^2+1^2}=\sqrt{2}. The incenter coordinates (x,y) are given by (\frac{ax_1+bx_2+cx_3}{a+b+c}, \frac{ay_1+by_2+cy_3}{a+b+c}). Thus x = \frac{2(1)+\sqrt{2}(0)+\sqrt{2}(2)}{2+2\sqrt{2}} = 1 and y = \frac{2(1)+\sqrt{2}(0)+\sqrt{2}(0)}{2+2\sqrt{2}} = \frac{1}{1+\sqrt{2}} = \sqrt{2}-1.

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