# Thread: Calculus .. Area Question

1. ## Calculus .. Area Question

An isosceles triangle is inscribed in a circle with radius one metre in such a way as to
maximize the area of the triangle. Determine its area. (Hint: Consider the area as a
function of the distance from the centre of the circle to the base of the triangle)

2. Originally Posted by sam126
An isosceles triangle is inscribed in a circle with radius one metre in such a way as to
maximize the area of the triangle. Determine its area. (Hint: Consider the area as a
function of the distance from the centre of the circle to the base of the triangle)
What have you tried? Where are you stuck?

3. $\displaystyle Area = \frac{base\cdot height}{2}$

If the distance to the base from the center of the circle is r, then the height of the triangle is $\displaystyle h=r+1$ since the radius of the circle is 1 and we assume that all corners of the triangle touch the circle. All the corners of the triangle will be at the distance r=1 from the center of the circle, so the base is going to have the length $\displaystyle \frac{b}{2}=\sqrt{1-r^2}$

So we have $\displaystyle Area = \frac{base\cdot height}{2}=(1+r)\sqrt{1-r^2}$