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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.
The circumcenter of a triangle is the center of the only circle that can be it?
circumscribed about
The circumcenter of a triangle is the center of the only circle that can be circumscribed about it?
True
In order to inscribe a circle in a triangle the circles center must be placed at the circumcenter of the triangle?
No.
The of a triangle is the center of the only circle that can be inscribed inside it?
incenter
Center of circle inscribed in a triangle?
The answer is circumcenter
What is the center of a circle inscribed in a triangle?
the answer is circumcenter
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.
The circumcenter of a triangle is the center of the only circle that can be inscribed about it?
False
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.
The incenter of a triangle is the center of the only circle that can be circumcised about it?
The statement is incorrect as it confuses the concepts of the incenter and circumcenter. The incenter is the center of the incircle, which is the circle inscribed within a triangle, tangent to its sides. The circumcenter, on the other hand, is the center of the circumcircle, which passes through all the triangle's vertices. Therefore, the incenter is related to the triangle's interior, while the circumcenter pertains to its exterior.
Is the center of the circumscribed circle about a triangle is equal distance to the vertices of the inscribed triangle?
Yes, the center of the circumscribed circle (circumcenter) of a triangle is equidistant from all three vertices of the triangle. This property holds true because the circumcenter is defined as the point where the perpendicular bisectors of the sides of the triangle intersect. Consequently, each vertex of the triangle lies on the circumference of the circumscribed circle, maintaining equal distances from the circumcenter to each vertex.
Why is it called circumcenter?
The circumcenter of a triangle is the center of a circle circumscribed around a triangle with each of the vertices of the triangle touching the circumference of the circle.
If a circle is circumscribed about a triangle the center of the circle is called the of the triangle?
Centre
Is the circumcenter of a triangle the center of the circle circumscribed about the triangle?
Yes.
What is the circumcenter of a triangle?
Circumcenter - the center of the circle that circumscribes the triangle, ie. goes through all its vertices.
The circumcenter of a triangle is the center of the only circle that can be it?
circumscribed about
