1. Project of group 3: Incircle and Excircle Given 3 points in the coordinate system: A(0, 0), B(4, 0), C(1, 3).
Show that the center of the nine-point circle is on the Euler line (use the results of projects of group 1 & 2 to do).
Use formula to find the coordinates of incenter, and write equation of the incircle of triangle ABC in center-radius form.
In the formula (xa, ya), (xb, yb), (xc, yc) are coordinates of points A, B and C; a, b, c are the lengths of the 3 sides; P is the perimeter of the triangle.

2. Project of group 3: Incircle and Excircle Given 3 points in the coordinate system: A(0, 0), B(4, 0), C(1, 3).
Show that the incircle is tangent to the nine-point circle. Use 2) and results of group 2 to do.
Write the equation of the A-excircle and show that the excircle is tangent to the nine-point circle. Use results of group 2 to do.