Find the area of the largest isosceles triangle that can be inscribed in a circle of radius r = 14 (see figure).

Question

Solve for the area, and write as a function of h and then as a function of a.

Answer 1

There's no figure, but maybe we can still solve this.

Draw in the base of the triangle at some random location near the bottom of the circle. Then draw a vertical line bisecting the base---this line will go through the center of the circle. The base is a chord of the circle and is related to the distance from the center. We can therefore define both the chord length and the height of the triangle as a function of the distance from the center of the circle to the chord.

From this, write the equation for the area of the triangle as a function of the distance from chord to center of the circle.

Find the maximum area by taking the 1st derivative of this equation and setting = to 0.

I'll try it later if someone doesn't beat me to it.....

Answer 2