Problem:
Two tangents to a circle are drawn from a point . The points of contact and divide the circle into arcs with lengths in the ratio . What is the degree measure of ?
Answer Choices:
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Solution:
Let be the center of the circle, and let the degree measures of the minor and major arcs be and , respectively. Because , it follows that and . In quadrilateral , the segments and are tangent to the circle, thus and .
The problems on this page are the property of the MAA's American Mathematics Competitions