Optimization Problem: Isosceles Triangle Circumscribed about a Circle
Suppose a circle has radius of 25 feet.
Suppose an isosceles triangle is drawn around this triangle so that each of its 3 sides is tangent to this circle. (Such a triangle is said to be circumscribed about the circle.)
If this is the case, use calculus to determine the dimensions (height and base) of such a triangle that minimizes the triangle's area. Also, prove that these actual dimensions minimize the area of this triangle.