¶ 1995 AHSME Problem 18
Problem:
Two rays with common endpoint form a angle. Point lies on one ray, point on the other ray, and . The maximum possible length of is
Answer Choices:
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B.
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E.
Solution:
By the Law of Sines, , so , with equality if and only if .
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Consider to be fixed on a ray originating at a variable point , and draw another ray so the angle at is . A possible position for is any intersection of this ray with the circle of radius centered at . The largest value for for which there is an intersection point occurs when is tangent to the circle. Since is a triangle with , it follows that is largest.
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