This is true, by definition.
Assume that there is a circle that passes through each vertex of a triangle. Then its centre, which we may call the circumcentre of the triangle, must be at an equal distance from each of the vertices because all of the points of the circle are at the same distance from this point.
Circumcenter. The circumcenter of a triangle is the center of the circumcircle of the triangle. It is the point, O, at which the perpendiculars bisectors of the sides of a triangle are concurrent. The circumcircle of a triangle is the circle that passes through the three vertices. Its center is at the circumcenter.
No way! An easy example is the centroid and circumcenter of a right-angle triangle. Circumcenter will be exactly on the middle of the hypotenuse which obviously cannot be the centroid. Centroid is the point where all three lines are connecting all the three vertices and the middle of the line opposite the respective vertex. Circumcenter is the center of the circle passing through all the vertices. As it is known, a right-angle triangle will always fall within a semicircle, meaning the circle center will always be on the middle of the hypotenuse.
sides
Figure A three vertices-> triangle
30, its a combination. C(6,3) because there are six vertices of a hexagon and three vertices of a triangle
equidistant from the vertices
It is called the circumcenter of the triangle. . The circumcenter is equidistant from the three vertices, and so the common distance is the radius of a circle that passes through the vertices. Another name for it is the circumcircle
circumcenter
The circumcenter of a triangle is the center of the circle drawn outside the triangle with all three vertices touching its circumference.
Circumcenter. The circumcenter of a triangle is the center of the circumcircle of the triangle. It is the point, O, at which the perpendiculars bisectors of the sides of a triangle are concurrent. The circumcircle of a triangle is the circle that passes through the three vertices. Its center is at the circumcenter.
The point equidistant from the three sides of a triangle is the center of the triangle. The center of the triangle is the point of intersection of the medians of the triangle. The medians of a triangle are the line segments that join the vertices of the triangle to the midpoints of the opposite sides.
No way! An easy example is the centroid and circumcenter of a right-angle triangle. Circumcenter will be exactly on the middle of the hypotenuse which obviously cannot be the centroid. Centroid is the point where all three lines are connecting all the three vertices and the middle of the line opposite the respective vertex. Circumcenter is the center of the circle passing through all the vertices. As it is known, a right-angle triangle will always fall within a semicircle, meaning the circle center will always be on the middle of the hypotenuse.
I think it's circumcenter of the triangle if you stare at the question long enough. Like where the the three ?vertices? are meeting in the middle.
It identifies the point which is equidistant from the three vertices of the triangle. If, for example, you wanted to locate a phone mast to supply three remote locations, a good starting point would be to find somewhere which is at or very close to the circumcentre. Of course, local geography (hills, for example) would have to be taken into account.
sides
A triangle has three sides and therefore three vertices, or angles.
The circumcenter of a triangle is the center of a circle who's radius touches all three of the triangle's vertices. The circumcenter can be found using the intersection of 2 or more perpendicular bisectors. A bisector is a line perpendicular from the mid point of a triangle's line segment.To find the circumcenter of a triangle, create two bisectors by following these steps:StepsWith a compass, draw a circle from the first point in the triangle larger then the triangle.Draw the same size circle from point two.Draw the same size circle from point three.Draw a line from the two intersecting points of circle one and two.Draw a line from the two intersecting points of circle two and three.The intersection of the lines from step 4 and 5 will define the circumcenter of the triangle.