The attached diagram (taken from this Wikipedia page) shows what Pólya means. The red lines are the "internal bisectors" of the angles of the triangle ABC. The green lines (each green line is perpendicular to the red line through the same vertex) are the "external bisectors" of those angles. The blue circle is the inscribed circle. The three yellow circles are the escribed circles. Each escribed circle touches one side of the triangle internally, and the other two sides externally (in other words, when they are extended beyond the original triangle).

The four points of intersection are the points where three of the red or green lines intersect. These points are I, the incentre, and , the three excentres.