8 The number of al possible triangles in the given figure is: MATHEMATICS OLYMPIAD fis (A) 30 (B) 34 (C) 26 (D) 24 (E) 20

1. Let the vertices of the large triangle be \(A\), \(B\), and \(C\). Suppose that points \(D\), \(E\), and \(F\) are the midpoints of \(BC\), \(AC\), and \(AB\), respectively, and that the medians \(AD\), \(BE\), and \(CF\) are drawn. Their intersection is the centroid \(G\). 2. The medians divide the triangle into 6 small regions whose boundaries are parts of the original sides and the medians. These 6 “small” triangles are visible immediately. 3. In addition to these 6 basic triangles, many larger triangles appear in the figure. For example, the segments drawn allow triangles whose vertices are chosen among \(A\), \(B\), \(C\), \(D\), \(E\), \(F\), and \(G\) provided that every side is one of the drawn segments. 4. A careful classification (by grouping regions or by listing all triangles with vertices chosen among the 7 points while discarding those having a “broken” side) shows that the total number of triangles that occur in the figure is 24. 5. Since 24 is one of the options, the correct answer is \[ 24. \]