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If you click the nearby link and look at the figure on the left, that's a pentagram -- a five-pointed star inscribed within a pentagon. Label the five vertices A, B, C, D, E, and F. Label the five interior line intersections G, H, I, J, and K. Can't you see how many triangles are formed by the lines? Look at point A. ABC defines one triangle, ABD defines another, and ABE defines yet another. That's three already just starting with point A. There are four others that use point A and one or two of the interior points. So, each point of the star is contained in seven triangles.

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