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Why is the center of a circle inscribed in a triangle always the incenter?

That is the definition of the incenter; it is the center of the inscribed circle.


What is incenter of triangle?

It is the center of the circle that is inscribed in the triangle.


Is the incenter of a triangle the center of the circle circumscribed about the triangle?

No.


If a circle is inscribed in a triangle the center of the circle is called the what of the triangle?

The circumcenter of the triangle.


What is the blank of a triangle is the center of the circle inscribed in the triangle?

incenter


In order to circumscribe a circle about a triangle the circle's center must be placed at the incenter 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.


If a circle is inscribed in a triangle the center of the circle is called?

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.


If a circle is inscribed in a triangle the center of the circle is called the?

If a circle is inscribed in a triangle, the center of the circle is called the incenter. The incenter is the point where the angle bisectors of the triangle intersect, and it is equidistant from all three sides of the triangle. This point serves as the center of the inscribed circle, known as the incircle.


In order to circumscribe a circle in a triangle the circle's center must be placed at the incenter of the triangle?

False!


In order to inscribe a circle in a triangle the circle's center must be placed at the incenter of the triangle?

That is correct


The of a triangle is the center of the only circle that can be inscribed inside it?

incenter


The incenter of a triangle is the center of the only circle that can be inscribed in it?

true