A triangle are the lines that divide each angle of the triangle into two equal parts, with one part inside the triangle and the other part outside the triangle. The external bisectors are also known as the external angle bisectors.

These lines meet at a point called the excenter of the triangle. The excenter is the center of an excircle of the triangle, which is a circle that is tangent to one side of the triangle and to the extensions of the other two sides.

The external bisectors have several important properties. First, they are concurrent, meaning they all intersect at a single point. This point is the excenter of the triangle. Second, the external bisectors divide the exterior angles of the triangle into two equal parts. This means that the measure of each exterior angle is twice the measure of the adjacent interior angle.

The external bisectors also have a relationship with the internal bisectors of the triangle. The external bisectors and internal bisectors are perpendicular to each other. This means that the internal bisectors form right angles with the external bisectors at the excenter of the triangle.

The external bisectors are useful in various geometric constructions and proofs. They can be used to find the excenter of a triangle, which can be helpful in determining the properties of the triangle and its excircles. They can also be used to prove various properties of triangles, such as the angle bisector theorem and the properties of isosceles triangle.