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Is this statement true or falseThe circumcenter of a triangle is the center of its circumscribed circle?
true
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Is this statement true or falseThe circumcenter of a triangle is the point of concurrency of the angle bisectors of a triangle?
false
Is this statement true or falseThe circumcenter of a right triangle always lies on the hypotenuse?
true
Is the circumcenter of a triangle the center of the circle circumscribed about the triangle?
Yes.
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 this statement true or falseThe circumcenter of an obtuse triangle lies inside the triangle?
false
Is this statement true or falseThe circumcenter of a triangle is the point of concurrency of the angle bisectors of a triangle?
false
Is this statement true or falseThe circumcenter of a right triangle always lies on the hypotenuse?
true
Is the circumcenter of a triangle the center of the circle circumscribed about the triangle?
Yes.
The circumcenter of a triangle is the center of the only circle that can be it?
circumscribed about
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
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.
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.
True or False The circumcenter of a triangle is the center of the only circle that can be circumscribed about it.?
true!
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.
