Maximum Radius of Circle
Optimization Problem with Solution

Use the derivative to find the size of an angle of a right triangle so that the radius of the circle inscribed is maximum; for a constant hypotenuse.


ABC is a right triangle and r is the radius of the inscribed circle.
a) Express r in terms of angle x and the length of the hypotenuse h.
b) Assume that h is constant and x varies; find x for which r is maximum.

circle inscribed in triangle for the problem

Solution to Problem:

More references on calculus problems