Extended side

excircles (orange) is tangent

to one of the triangle's sides and to the other two extended sides.

In

of the polygon. The extension of a finite side into an infinite line arises in various contexts.

Triangle

In an

intersect the corresponding extended base sides but not the base sides themselves.

The

to one side and to the other two extended sides.

Trilinear coordinates locate a point in the plane by its relative distances from the extended sides of a reference triangle. If the point is outside the triangle, the perpendicular from the point to the sideline may meet the sideline outside the triangle—that is, not on the actual side of the triangle.

In a triangle, three intersection points, each of an

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In a triangle, three intersection points, two of them between an

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Ex-tangential quadrilateral

An

bisectors) at the other two vertex angles, and the external angle bisectors at the angles formed where the extensions of opposite sides intersect.

Hexagon

Pascal's theorem states that if six arbitrary points are chosen on a conic section (i.e., ellipse, parabola or hyperbola) and joined by line segments in any order to form a hexagon, then the three pairs of opposite sides of the hexagon (extended if necessary) meet in three points which lie on a straight line, called the Pascal line of the hexagon.

References