|
How to construct a line tangent to a given circle, through a given point on or outside that circle?
|
1. |
| Start with the given circle and point.
If the given point lies inside the circle, there is no such line.
First case: the given point lies on the circle.
|
|
2. |
| Draw the ray of the given circle from its center to the given point.
|
|
3. |
| Construct the line perpendicular to ray 2, passing through the given point.
This is the line to be constructed: it is passing though the given point and is tangent to the given circle.
|
|
4. |
| Case 2: the given point lies outside the given circle.
|
|
5. |
| Construct the "two-points" circle (defined by the two end-points of a centerline) between the given point and the center of the given circle.
|
|
6. |
| Draw two lines, from the given point to the two intersections of the given circle and circle 5.
|
|
7. |
| Lines 6 are the lines to be constructed. They pass through the given point, and are tangent to the given circle.
Notice, that there are two such lines!
|
|