CEMC Banner

Problem of the Week
Problem B
Something's Missing…

The figures in the diagram below are similar. They each contain a circle and some straight lines.

  1. Suppose new figures are created by removing all straight lines which lie outside the circle from 75\(\%\) of the figures.

    1. Draw a diagram showing what one of the new figures would look like.

    2. How many new figures are created?

    3. How many of the original figures remain unchanged?

  2. Now suppose that the circle is removed from \(\frac{2}{3}\) of the new figures created in part a).

    1. How many of the new figures from part a) will still contain a circle?

    2. Draw a diagram of one of the new figures with the circle removed. Then name all the geometric shapes formed by the straight lines in this figure.

There are 16 figures. Each figure is formed as follows: A hexagon is drawn with a circle passing through all of its six vertices. From each vertex of the hexagon, two straight lines are drawn outside the circle. From one vertex of the hexagon, two straight lines are drawn inside the circle joining it to two other vertices that are side by side.