### Instruction: Circle $C$ has radius 6 cm. How many square centimeters are in the area of the largest possible inscribed triangle having one side as a diameter of circle $C$?### Response: To find the area of the largest possible inscribed triangle, I need to think of what kind of triangle would have the maximum area given that one side is fixed as a diameter of the circle.
I recall that the area of a triangle is given by $\frac{1}{2}bh$, where $b$ is the base and $h$ is the height.
Since the base of the triangle is a diameter of the circle, its length is $2r = 12$ cm.
To maximize the height of the triangle, I want to choose the other two vertices of the triangle such that they are as far away from the diameter as possible.
I realize that this means the other two vertices must lie on the circle, and they must be symmetric about the diameter.
This means the triangle is actually a right triangle, and the height is equal to the radius of the circle, which is $6$ cm.
Therefore, the area of the triangle is $\frac{1}{2} \times 12 \times 6 = 36$ square centimeters.