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Did You Find Out? Get the Answer to the Riddle of E-News Issue No. 3, July 2020

2020-06-30

Dividing a Circular Area

Divide the circular area with four straight lines into as many pieces as possible.

At the end of a geometry lesson, a teacher presents his students with the following geometric puzzle: What is the maximum number of parts in which a circular area with four straight lines can be divided into and how do these lines have to be arranged? The parts do not necessarily have to be the same size. As an example, the teacher draws a circle with eight parts (see picture aside) on the board and adds that it is possible to get more than just these eight parts.

What is the maximum number of pieces you can divide the circle into?

Solution

You can use four straight lines to divide the circle into a maximum of 11 parts. This number is obtained by intersecting each line with every other line and by not having more than two lines intersect. A possible solution would be the following:

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