How many intersection points can be formed with 3 circles , 4 straight lines ?

Question

Answer

Given number of circles=3,
number of straight lines=4,
*Line line
as two lines can intersect each other at exactly one point So 4 lines intersect each other at,
4C2=4!/2!2!=6,
* line and circle,
a line and circle intersect each other at two points so3 circle and four circle can intersect each other at 2(4C1×3C1)=24,
* circle circle ,
as 2 circles can intersect at two points then three circles intersect each other at 10points.
total number of points of intersection=6+10+24=40

Answer

Answer

Intersections of Circles

To determine the number of intersection points formed by three circles, we need to consider the different scenarios that can occur between the circles.

Scenario 1: No Intersections

If the three circles do not intersect each other at any point, then the total number of intersection points would be zero.

Scenario 2: Pairwise Intersection

If the circles intersect each other pairwise, meaning that each circle intersects with the other two circles, we need to determine the number of intersection points between each pair of circles and then sum them up.

For two circles, the maximum number of intersection points is 2. Therefore, for three circles, the maximum number of intersection points between any two circles would be 2.

Since we have three pairs of circles, the maximum number of intersection points between the three circles would be 2 * 3 = 6.

Scenario 3: All Circles Intersect at One Point

If all three circles intersect at a single point, we need to determine the number of intersection points between each pair of circles and then sum them up.

For two circles intersecting at a single point, the number of intersection points is 1.

Since we have three pairs of circles, the number of intersection points between the three circles would be 1 * 3 = 3.

Scenario 4: Two Circles Intersect at One Point, Third Circle Intersects at Two Points

If two circles intersect at a single point and the third circle intersects those two points, we need to determine the number of intersection points between each pair of circles and then sum them up.

For the two circles intersecting at a single point, the number of intersection points is 1.

For the third circle intersecting those two points, the number of intersection points is 2.

Therefore, the total number of intersection points between the three circles would be 1 + 2 = 3.

Intersections of Straight Lines

To determine the number of intersection points formed by four straight lines, we need to consider the different scenarios that can occur between the lines.

Scenario 1: No Intersections

If the four straight lines do not intersect each other at any point, then the total number of intersection points would be zero.

Scenario 2: Pairwise Intersection

If the lines intersect each other pairwise, we need to determine the number of intersection points between each pair of lines and then sum them up.

For two lines, the maximum number of intersection points is 1. Therefore, for four lines, the maximum number of intersection points between any two lines would be 1.

Since we have six pairs of lines, the maximum number of intersection points between the four lines would be 1 * 6 = 6.

Scenario 3: All Lines Intersect at One Point

If all four lines intersect at a single point, we need to determine the number of intersection points between each pair of lines and then sum them up.

For two lines intersecting at a single point, the number of intersection points is 1.

Since we have six pairs of lines, the number of intersection points between the four lines would be 1 * 6 = 6.

Summary

In summary, for three circles, the maximum number of intersection points is 6, while

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