An Inscribed Circle in a Right Triangle

Dick Smith
This lesson allows students to study an inscribed circle in a right triangle. The circle has a fixed radius of 2. The lesson shows that there are two rational expressions that create the radius. Both are expressions tht simply use the legs and the hypotenuse. The lesson also shows the ratio of the circle area to the triangle area of the figure. The shape of the triangle can be changed by simply dragging the verted B point along the x-axis.
Can you use algebra to recreate the expressions that create the value of the radius? What is the largest value of the circle area to triangle area? What else can you tell your teacher about what you learned? What pythagorean triples can you find that are whole numbers?