



 
Hi Charlene, I let the diameter of the circle be d and the lengths of the other two sides of the triangle be x and y. The perimeter is then given by P = d + x + y.
What does your intuition tell you should be the position of the vertex V to maximize the perimeter? Can you convince yourself, without calculus, that this is the correct answer? The diameter d of the circle is a constant so P = d + x + y is a function of two variables x and y. To solve this problem using calculus you need to express P as a function of one variable. The key here is that the triangle is a right triangle since the angle subtended at the circumference of a circle by a diameter is a right angle. Pythagoras' theorem then gives you a relationship between x and y that allows you to express P as a function of one variable. Differentiate this expression and use you knowledge of calculus to maximize P. What is the position of V when the perimeter is maximized? was your intuition correct? Penny  


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences. 