¶ 1994 AHSME Problem 18
Problem:
Triangle is inscribed in a circle, and . If and are adjacent vertices of a regular polygon of sides inscribed in this circle, then
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Answer Choices:
A.
B.
C.
D.
E.
Solution:
Since , it follows that . Therefore, , which is of . Thus the polygon has sides.
If is partitioned into four angles congruent to , the four chords associated with the arcs subtended by these angles will be congruent to . These four chords plus four obtained analogously from , together with , form the sides of the inscribed regular polygon.
Note. In general, if , then .