Difference between revisions of "What is the greatest number of points of intersection that can occur when $2$ different circles and $2$ different straight lines are drawn on the same piece of paper?"
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Latest revision as of 17:11, 7 August 2020
What is the greatest number of points of intersection that can occur when different circles and different straight lines are drawn on the same piece of paper?
Solution 1:
Make a diagram. Two geometric figures intersect if they have one or more points in common. Draw two circles which intersect in points. Draw a line which intersects the two circles in points. Draw another line which intersects the two circles in points and also intersects the first line. There are points of intersection.[asy]
draw(Circle((-0.7,0),1)); draw(Circle((0.7,0),1));
dot((0,0));
dot((0,0.7)); dot((0,-0.7));
draw((0,0)--(-2,0.6),Arrow); draw((0,0)--(-2,-0.6),Arrow); draw((0,0)--(2,0.6),Arrow); draw((0,0)--(2,-0.6),Arrow);
dot((-1.58,0.47)); dot((-1.58,-0.47)); dot((1.58,0.47)); dot((1.58,-0.47));
dot((-0.29,0.08)); dot((-0.29,-0.08)); dot((0.29,0.08)); dot((0.29,-0.08));
[/asy] Solution 2: Make a table of the maximum number of points of intersection.