CIRCLE • LINE • LINE
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Diverging Lines Not Intersecting A Circle
Number of solutions: 4
GeoGebra construction
Steps
- Two intersecting lines and circle without contact
- We draw the angle bisector of the assigned lines. We mark the center of the assigned circle in the axial symmmetry with the use of the angle bisector. We connect
- both points with a line.
- We find the radius of the assigned circle and draw a circle with the same radius anywhere on one of the assigned lines.
- We draw two lines which are parallel with the assigned line and also are tangents of this new circle.
- We draw a circle defined by three points. The center of the assigned circle, the mirrored center of the assigned circle and an arbitrary point. We mark the point of
- intersection of one of the two tangents from step 3 and the line from step 1 which passes through the center of the assigned circle.
- We draw two lines which pass through the point of intersection from the previous step and are tangents of the circle from the previous step. We mark the intersection
- points of these lines with the cricle.
- We draw a circle defined by three points. One is the intersection point from step 4 and the two remaining are the intersections from the previous step.
- We draw a circle with the center in the intersection point from step 4 and defined by one of the interstection points from step 5. We mark two intersection points
- of this cricle with the line from step 3.
- We draw a line perpendicular to the assigned line and which passes through one of the intersection points from the previous step. To continue, we repeat this process but
- we use the second of the intersection points. We mark the intersection points of these lines with the assigned line and the angle bisector of the assigned lines.
- We draw two circles defined by a center and a point. Centers are the points of intersections on the angle bisector from step 8 and points are the points of intersections
- on the assigned line from the previous step.
- Now we will focus on the second of the two tangents from step 3. The process is the same. We find a point of intersection of the tangent and the line which passes
- through the center of the assigned circle and the mirrored center of the assigned circle.
- We draw two tangents on the circle from step 4 which pass through the point of intersection from the previous step. We mark the points of intersection of these lines with
- the circle from step 4.
- We draw a circle defined by three points. Two of these points are the points of intersection from the previous step and the last point is the point of intersection from
- step 10. Now we draw a circle with the center in the point of intersection from step 10 and defined by one of the points of intersection from step 11. We mark two points of
- intersection of this circle with the line from step 3.
- We draw a line perpendicular to the assigned line and which passes through one of the points of intersection from the previous step. We repeat thsi process but we use the
- second of these two intersection points. We mark the points of intersection of these lines with the assigned line and the angle bisector of the assigned lines.
- We draw two circles defined by a center and a point. The centers lie in the points of intersection on the angle bisector from the previous step and the points are the
- points of intersection on the assigned line from the previous step.
GeoGebra construction
Steps
- two divergent lines and a cricle without contact
- We draw a perpendicular line to the assigned straight lines that are going through the assigned circles and we mark the four points of intersection.
- We draw four straight lines parallel to the assigned straight lines that are going through the points of intersection from the previous step.
- We mark the four new points of intersections of these straight lines and we draw the angle bisector of between the assigned straight lines.
- We draw two straight lines that are going through the point of intersection of the assigned straight lines and the points of intersection L and N. We mark the points of intersection of these new straight lines with the assigned circle.
- We draw straight lines taht are going through the centre of the assigned circle and one of these new points of intersection. We repeat this for each of the four points of intersection.
- We mark the points of intersection of these new straight lines with the angle bisector of the assigned straight lines.
- We draw a circle defined by a point and a centre. The centre is located in the points of intersections from the previous step. As a point serve the points of intersection on the circle from step 5. The point and centre of each of the four circles is located on the same straight line from step 6.