Drag the base angle slider to change the base angle of the isosceles triangle, or hit the start button to animate.[br][br]If the length of each leg is 1, the area of the incircle, which is tangent to all three sides, is maximal when the base length is sqrt(5) - 1 and the base angle is the inverse cosine of ((sqrt(5) - 1) / 2).[br][br]Challenge problem: use calculus to prove the above statement. It will be very helpful to use the fact that the area of the triangle equals one-half times the radius of the incircle times the perimeter of the triangle, along with Heron's formula.