"Circumcenters" Example Sentences
1. The circumcenters of all triangles lie on the circumcircle.
2. The circumcenters of obtuse triangles lie on the extension of the base.
3. The circumcenters of right triangles lie on the midpoint of the hypotenuse.
4. The circumcenters of acute triangles lie inside the triangle itself.
5. The circumcenters of isosceles triangles lie on the perpendicular bisector of the base.
6. The circumcenters of scalene triangles lie at different positions based on the side lengths.
7. The circumcenters of equilateral triangles coincide with their centroid and orthocenter.
8. A set of collinear circumcenters can exist only in the case of a straight line.
9. The circumcenters of a cyclic quadrilateral are the intersections of the perpendicular bisectors.
10. The circumcenters of a regular polygon lie on a circle that passes through the vertices.
11. The circumcenters of a parallelogram are located outside the figure.
12. The circumcenters of an isosceles trapezoid lie on the perpendicular bisector of the non-parallel sides.
13. The circumcenters of a kite coincide with its diagonals intersection.
14. The circumcenters of an equidiagonal quadrilateral are the same as the regular quadrilateral.
15. The circumcenters of a rectangle lie on its axes of symmetry.
16. The circumcenters of a square are the midpoints of its sides.
17. The circumcenters of an equilateral triangle and its medial triangle are the same point.
18. The circumcenters of similar triangles are located on the same line.
19. The circumcenters of a triangle and its orthic triangle are collinear.
20. The circumcenters of a triangle and its Excentral triangle lie on a circle with the nine-point center.
21. The circumcenters of the outer triangles in Soddy's hexlet lie on a circle with the incircle center.
22. The circumcenters of the contact triangles lie on the perpendicular bisectors of the sides.
23. The circumcenters of a cyclic pentagon lie on a circle that passes through the vertices.
24. The circumcenters of a Trapezoidal hexagon are located on the same circle that passes through the midpoints of the non-parallel sides.
25. The circumcenters of Pappus Hexagon lie on a circle that passes through the midpoints of the opposite sides.
26. The circumcenters of a right kite lie at the intersection of the diagonals.
27. The circumcenters of a concyclic polygon lie on a circle that passes through all its vertices.
28. The circumcenters of a Lemoine Hexagon lie on the circle that passes through the two triangles formed by joining three consecutive vertices each.
29. The circumcenters of a choral Pentagon lie on a circle with the Six-point center.
30. The circumcenters of a triangle and its circumcevian triangle are collinear.
Common Phases
not have any idea how to start solving problems involving
circumcenters; always make sure to draw the circumcircle first before trying to find the circumcenter; the circumcenter is the point where the perpendicular bisectors of the sides of a triangle meet; in an equilateral triangle, the circumcenter is also the centroid and orthocenter; knowing the circumcenter can help solve problems involving the distance from the vertices to the circumcenter; important formula to remember: distance from circumcenter to vertex = circumradius.