Henry Ernest Dudeney/Puzzles and Curious Problems/240 - Counting the Triangles

by : $240$

 * Counting the Triangles
 * Draw a pentagon, and connect each point with every other point with straight lines, as in the diagram.


 * Dudeney-Puzzles-and-Curious-Problems-240.png


 * How many different triangles are contained in this figure?


 * To make it quite clear, $AFB$, $AGB$, $ACB$, $BFG$, $BFC$, and $BGC$ are six such triangles.


 * It is not a difficult count if you proceed with some method,
 * but otherwise you are likely to drop triangles or include some more than once.