There is only one possible circle that can be inscribed in any triangle because all of the sides of the triangle must touch the circle at some point. Also, there is only one "incenter" of each circle. The incenter is the center of an inscribed circle.
Only one to which all three sides are tangents. If you remove that requirement, then infinitely many.
Exactly one circle can be inscribed in a given triangle.Many triangular shapes can be inscribed in a given circle.
Only one circle will touch all three sides.
Yes, that is correct. Circles circumscribed about a given triangle will have centers that are equal to the incenter, which is the point where the angle bisectors of the triangle intersect. However, the radii of these circles can vary depending on the triangle's size and shape.
False
false
Flat piece of inscribed metal given as an honor or reward
A scalene triangle would fit the given description
infinite.. you can have different sizes of circles crossing at the same point.. so it can literally be an infinite amount
You cannot show it in general since it need not be true!
true
the circle is inscribed in the polygon :]
The description given fits that of a scalene triangle.