A rectangle, a circle and a triangle are drawn in a plane. What is the maximum number possible points of intersection. The sides of the triangle are not collinear with any of the sides of the rectangle.
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To find the maximum number of points of intersection, we need to consider the different combinations of shapes intersecting with each other.
Let's analyze the possible intersections one by one:
1. Rectangle and Circle:
- A rectangle can intersect a circle at a maximum of 8 points: 4 corners and 4 possible points on the sides where the circle and rectangle touch.
- However, in this case, the sides of the triangle are not collinear with any of the sides of the rectangle, so there will be no intersection points between the rectangle and the circle.
2. Triangle and Circle:
- A triangle can intersect a circle at a maximum of 6 points: one at each triangle vertex and three times where each side of the triangle intersects with the circle.
- However, in this case, there is no information given about the size or position of the triangle, so we cannot determine the exact number of intersection points. It could be 0, 1, 2, 3, 4, 5, or 6 points.
3. Triangle and Rectangle:
- A triangle can intersect a rectangle at a maximum of 6 points: one at each triangle vertex and three times where each side of the triangle intersects with the rectangle.
- Similarly to the above case, without additional information about the size or position of the triangle and rectangle, we cannot determine the number of intersection points precisely.
Considering each possible intersection mentioned above, the maximum number of points of intersection would be 8, but in this particular scenario where the sides of the triangle are not collinear with any of the sides of the rectangle, there would be no intersection points.
Hence, the maximum number of intersection points in this case is 0.
well, the triangle's 3 sides can each intersect with two sides of the rectangle, making six intersections.
Now see what you can do with the circle.