Hello, aaasssaaa!

Here's my approach to this problem . . .

Find the dimensions of the isosceles triangle of largest area

that can be inscribed in a circle of radius r. Code:

A
* * *
* : *
* : *
* r: *
:
* : *
* * *
* : \ *
y: \r
* : \ *
B* - - - + - - - *C
* x *
* * *

Draw line segments and

We will maximize the area of

. . which has base and height

The area of the triangle is: . **[1]**

Using Pythagorus, we have: . **[2]**

Substitute [2] into [1]: .

Differentiate: .

Equate to zero: .

Multiply by

Then we have: .

Square both sides: .

. .

If , we have which produces __minimum__ area . . . *ha!*

If , we have: .

Substitute into [2] and we get: .

Therefore, the triangle has: .

Note: The triangle happens to be *equilateral*,

. . . . .which you may have suspected all along.