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.