That is correct
That is correct
To inscribe a circle in a triangle, first, find the triangle's three angle bisectors. The point where these bisectors intersect is called the incenter, which serves as the center of the inscribed circle. Next, measure the perpendicular distance from the incenter to any side of the triangle; this distance is the radius of the inscribed circle. Finally, draw the circle using the incenter as the center and the measured radius.
No.
Of course not! There are an infinite number of smaller circles.
It is the center of the circle that is inscribed in the triangle.
No.
That is the definition of the incenter; it is the center of the inscribed circle.
incenter
No, there are two circles (incircle, circumcircle) associated with triangles and in general the locations of their centres are different.
The circumcenter of the triangle.
This statement is incorrect. To circumscribe a circle around a triangle, the circle's center must be located at the circumcenter, not the incenter. The circumcenter is the point where the perpendicular bisectors of the triangle's sides intersect, while the incenter is the point where the angle bisectors meet and is the center of the triangle's inscribed circle.
The center of the circle inscribed in a triangle is called the incenter. It is the point where the angle bisectors of the triangle intersect and is equidistant from all three sides of the triangle. The incenter is also the center of the incircle, which is the largest circle that can fit inside the triangle.