# Demonstration for constructing a tangent to a circle

- Author:
- gilad

- Topic:
- Circle

**Demonstration for constructing a tangent to a circle through a given point on it, with a straightedge only**Description of the construction Let A be the point on the circle through which a tangent shall be drawn. Select any five points on the circle B, C, D, E and F. By using the GeoGebra-Dynamic Geometric Software, construct the chords AC, AD, BD, BE and CE. Point K denote the point of intersection of the chords AC and BD. Point L denote the point of intersection of the chords AD and EC. Connect the points K and L by a straight line. The continuation of the straight line LK intersects the continuation of the chord BE at the point P. The straight line connecting the points P and A is the sought tangent AP. As the point F is dragged toward the point A, the location of the points P, K, L remain on one straight line remain on the same one straight line. When point F coincides with the point A, the hexagon degenerates and the line FP becomes a tangent. Note: if the straight lines KL and BE are parallel or almost parallel, its need to change slightly the position of point B and continue the construction as described.

**Demonstration for constructing a tangent to a circle through a given point on it, with a straightedge only**Description of the construction Let A be the point on the circle through which a tangent shall be drawn. Select any five points on the circle B, C, D, E and F. By using the GeoGebra-Dynamic Geometric Software, construct the chords AC, AD, BD, BE and CE. Point K denote the point of intersection of the chords AC and BD. Point L denote the point of intersection of the chords AD and EC. Connect the points K and L by a straight line. The continuation of the straight line LK intersects the continuation of the chord BE at the point P. The straight line connecting the points P and A is the sought tangent AP. As the point F is dragged toward the point A, the location of the points P, K, L remain on one straight line remain on the same one straight line. When point F coincides with the point A, the hexagon degenerates and the line FP becomes a tangent. Note: if the straight lines KL and BE are parallel or almost parallel, its need to change slightly the position of point B and continue the construction as described.