Problem:
Points and are on a circle of radius and . Point is the midpoint of the minor arc . What is the length of the line segment ?
Answer Choices:
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Solution:
Let be the center of the circle, and let be the intersection of and . Because bisects minor arc is a perpendicular bisector of chord . Hence , and applying the Pythagorean Theorem to yields . Therefore , and applying the Pythagorean Theorem to yields
The problems on this page are the property of the MAA's American Mathematics Competitions