Grades 9-10 Video Solutions 2013-Level 9&10 Video Solutions 2013 problem27

Level 9&10 Video Solutions 2013 problem27

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Video Summary

To find the number of triangles containing the center O of a regular 13-sided polygon inscribed in a circle, split the circle with a diameter creating arcs with six and seven vertices each. Select two farthest vertices from the arc with seven vertices to form one triangle side, with the third vertex from the arc with six vertices. There are 7 ways to select two farthest vertices and 13 positions for the third vertex due to rotational symmetry of the polygon, resulting in 7 x 13 = 91 such triangles. Thus, 91 triangles contain the center O.

Keywords

triangles

center O

13-sided polygon

circle

rotational symmetry