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The center of the circumscribed circle lies on line segment and the longest side of the triangle is equal to the o?
If the center of the circumscribed circle (circumcenter) lies on a line segment of the triangle, it indicates that the triangle is isosceles or degenerate. In an isosceles triangle, the circumcenter lies along the line segment connecting the apex to the midpoint of the base. If the longest side of the triangle is equal to the circumradius, it suggests a specific relationship between the triangle's dimensions and its circumcircle. This scenario can occur in certain configurations, but further clarification is needed for a complete analysis.
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Is the incenter of a triangle the center of the circle circumscribed about the triangle?
No.
Is the circumcenter of a triangle the center of the circle circumscribed about the triangle?
Yes.
If a circle is circumscribed about a triangle the center of the circle is called the of the triangle?
Centre
Is this statement true or falseThe circumcenter of a triangle is the center of its circumscribed circle?
true
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.
Is the incenter of a triangle the center of the circle circumscribed about the triangle?
No.
Is the circumcenter of a triangle the center of the circle circumscribed about the triangle?
Yes.
The of a triangle is the center of the only circle that can be circumscribed about it.?
no
The circumcenter of a triangle is the center of the only circle that can be it?
circumscribed about
The center of the circumscribed circle about a triangle is equidistant to the vertices of the inscribed triangle?
true
If a circle is circumscribed about a triangle the center of the circle is called the of the triangle?
Centre
The point of concurrency for perpendicular bisectors of any triangle is the center of a circumscribed circle?
Yes, that's correct. The point of concurrency for the perpendicular bisectors of a triangle is called the circumcenter, and it is the center of the circumscribed circle of the triangle.
The circumcenter of a triangle is the center of the only circle that can be circumscribed about it?
True
Is the circumcenter of a triangle the center of the only circle that can be circumscribed?
Yes, it is.
What would the center of a circle which is circumscribed about a triangle be called?
The center of the circle. Perhaps clarify the question?
Is this statement true or falseThe circumcenter of a triangle is the center of its circumscribed circle?
true
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.
