"Incenters" Example Sentences
1. The incenters of triangles always lie inside the triangle itself.
2. If a triangle is equilateral, then all the incenters coincide.
3. The incenters of an isosceles triangle lie on the perpendicular bisector of the base.
4. The incenters of a scalene triangle are not collinear.
5. The incenter is the point of concurrency of the angle bisectors of a triangle.
6. The incenters of the three smaller triangles formed by the angle bisectors of a triangle are collinear.
7. The incenters of a square lie on its diagonals.
8. The incenters of regular polygons lie at the intersection of the perpendicular bisectors of the sides.
9. The incenters of congruent triangles are always the same point.
10. The incenters of concentric circles are coincident.
11. The incenters of a trapezoid lie on the line containing the segment connecting the midpoints of the non-parallel sides.
12. The incenters of the three outer triangles formed by constructing the tangent to a circle from a point outside it, are collinear.
13. The incenters of the four smaller triangles formed by joining the midpoints of the sides of a quadrilateral are collinear.
14. The incenters of the four triangles formed by the diagonals of a convex quadrilateral are collinear.
15. The incenters of a parallelogram lie on the diagonals.
16. The incenters of three mutually tangent circles are collinear.
17. The incenters of a triangle and its excentral triangle are concyclic.
18. The incenters of a right triangle lie on the hypotenuse.
19. The incenters of a cyclic quadrilateral lie on a circle passing through its vertices.
20. The incenters of a cyclic pentagon are concyclic.
21. The incenters of a cyclic hexagon are equidistant from the center of the circle.
22. The incenters of a rectangle are equidistant from two opposite vertices.
23. The incenters of a regular hexagon are the same as its circumcenter.
24. The incenters of a square and its nine-point circle are coincident.
25. The incenters of a tangential trapezoid are collinear with its midpoint.
26. The incenters of any three adjacent internal triangles of a regular polygon are collinear.
27. The incenters of any four adjacent internal triangles of a regular polygon are concyclic.
28. The incenters of the four triangles formed by any pair of opposite sides of a parallelogram are collinear.
29. The incenters of the triangles formed by any three non-collinear points on a circle are collinear.
30. The incenters of a kite lie on a line parallel to its short diagonal and equidistant from its long diagonal.
Common Phases
1. The
incenters of a triangle are equidistant to its sides;
2. The
incenters of an equilateral triangle coincide with its center;
3. The
incenters of a right triangle lie on its hypotenuse;
4. The
incenters of a triangle form the vertices of its incenter circle;
5. The
incenters of similar triangles are similar themselves;
6. The
incenters of a triangle form an orthocentric system with its altitudes;
7. The
incenters of an isosceles triangle are lies on the perpendicular bisector of its base.