How can you check if a point is the circumcenter of a triangle?

Check if the point is at the same distance from all the vertices of the triangle.

Check if any of the perpendicular bisectors of the triangle passes through the point.

Check if the point is the point of intersection for the angle bisectors of the triangle.

Check if the point is the center of the largest circle that can be drawn inside the triangle.

Question

How can you check if a point is the circumcenter of a triangle?

 Check if the point is at the same distance from all the vertices of the triangle.

 Check if any of the perpendicular bisectors of the triangle passes through the point.

 Check if the point is the point of intersection for the angle bisectors of the triangle.

 Check if the point is the center of the largest circle that can be drawn inside the triangle.

asnaseer · Answer

this site should help you answer your question: http://www.mathopenref.com/trianglecircumcenter.html

anonymous · Answer

it didn't actually . .

anonymous · Answer

check the distance from that point to all three vertices of your triangle.  if they are all the same then that point is the circumcenter.

anonymous · Answer

use the distance formula for distance.

asnaseer · Answer

that site states:

"One of several centers the triangle can have, the circumcenter is the point where the perpendicular bisectors of a triangle intersect. The circumcenter is also the center of the triangle's circumcircle - the circle that passes through all three of the triangle's vertices. As you reshape the triangle above, notice that the circumcenter may lie outside the triangle."

the answer is in that paragraph.

anonymous · Answer

thank you guysss !

anonymous · Answer

yw..