Practice Intersection (Geometric) in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
The set of all points where two or more geometric objects (lines, planes, curves) meet or cross each other.
Where two roads cross—that single crossing point is their intersection.
Showing a random 20 of 50 problems.
Example 1
mediumFind the intersection of and .
Example 2
easyDo lines and intersect? Explain why or why not.
Example 3
easyA line can cross a circle in at most how many points?
Example 4
easyIn a plane, a line can intersect a triangle in at most ___ points.
Example 5
mediumFind the intersection points of and the circle .
Example 6
mediumFind the intersection of and .
Example 7
mediumFind the intersection point(s) of line and circle . Classify the intersection (secant, tangent, or no intersection).
Example 8
mediumThree lines pass through a single common point. How many distinct intersection points are there?
Example 9
mediumFor what value of do the lines and NOT intersect?
Example 10
hardLines and meet on the line . Find .
Example 11
easyWhere does the line cross the -axis? Where does y=3x−6 cross the x-axis?
Example 12
easyWhere does cross the -axis?
Example 13
mediumFind where the line meets the circle . Find where y=0 meets the circle x²+y²=25.
Example 14
mediumHow many intersection points do 4 lines have if no two are parallel and no three meet at a point?
Example 15
mediumFind the intersection of and algebraically. Find the intersection of the two lines algebraically.
Example 16
hardWhere does meet ?
Example 17
easyHow many points are in the intersection of a circle with itself?
Example 18
challengeExplain why the intersection of two surfaces in 3D is generally a curve, not a point, using dimensions.
Example 19
easyWhere do the lines and intersect? Find where x=4 and y=7 intersect.
Example 20
mediumHow many intersection points do 5 lines have if no two are parallel and no three meet at a point?