Circle and Quad

Geometry Level 2

What is the maximum number of intersection points that a quadrilateral and a circle can have?


The answer is 8.

Rubayat Jalal by Rubayat Jalal , 29, Bangladesh

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

2 solutions

Zach Abueg
May 25, 2017

A straight line segment can meet a circle twice. A quadrilateral has 4 4 straight line segments; this gives us an upper bound: 8 8 maximum intersection points.

To demonstrate that it is possible to intersect all four sides in two places each, imagine a square, with a circle that has the same center and a diameter that’s just slightly larger than the width of the square, as shown below.

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Very nice. And that shows us how to generalize the problem :)

Calvin Lin Staff - 4 years ago
Rubayat Jalal
May 25, 2017

The quad is not needed to be convex! A quad has four sides. Each side can have at most two intersection point with the circle.The crossed quad ABCD meets this requirement. A N S 8 ANS\ \boxed{8}

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Can you also add a non-self-intersecting example?

Calvin Lin Staff - 4 years ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...