| 11. | The centre of the incircle, called the incentre, can be considered a centre of the polygon.
|
| 12. | The section characterizations below states what necessary and sufficient conditions a quadrilateral must satisfy to have an incircle.
|
| 13. | Every triangle is a circumgonal region because it circumscribes the circle known as the incircle of the triangle.
|
| 14. | In this case both midpoints and the center of the incircle coincide and by definition no Newton line exists.
|
| 15. | Given any triangle ABC, and any point M on BC, construct the incircle and circumcircle of the triangle.
|
| 16. | A tangential polygon has each of its sides tangent to a particular circle, called the incircle or inscribed circle.
|
| 17. | A circle inscribed in any polygon is called its incircle, in which case the polygon is said to be a tangential polygon.
|
| 18. | Feuerbach's theorem states that the nine-point circle is tangent to the incircle and the three excircles of a reference triangle.
|
| 19. | For any regular polygon, the relations between the common incircle, and the radius " R " of the circumcircle are:
|
| 20. | Dimensions related to an ideal triangle and its incircle, depicted in the Beltrami Klein model ( left ) and the Poincar?disk model ( right)
|
