Circles in Triangles: Geometric Construction

Draw a triangle with its incircle and excircle. First create a triangle with three visible sides. Then draw a circle inside the triangle that is tangent to all three sides, with its center at the incenter of the triangle. Next, draw a circle outside the triangle that is tangent to the extensions of all three sides, with its center at the excenter. Show the points where the circles touch the sides, and demonstrate how the incircle radius is smaller than the excircle radius. The overall diagram should illustrate the geometric relationship between triangles and circles, suitable for middle or high school mathematics instruction.