Point O is the center of the circle above, and the measure of is . If the length of is 18, what is the length of arc ?
A
B
C
D
Correct answer: B
Explanation
Choice B is correct. Because segments OA and OB are radii of the circle centered at point O, these segments have equal lengths. Therefore, triangle AOB is an isosceles triangle, where angles OAB and OBA are congruent base angles of the triangle. It’s given that angle OAB measures . Therefore, angle OBA also measures . Let represent the measure of angle AOB. Since the sum of the measures of the three angles of any triangle is , it follows that , or . Subtracting from both sides of this equation yields , or radians. Therefore, the measure of angle AOB, and thus the measure of arc , is radians. Since is a radius of the given circle and its length is 18, the length of the radius of the circle is 18. Therefore, the length of arc can be calculated as , or .
Choices A, C, and D are incorrect and may result from conceptual or computational errors.
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id cb_question_bank:3bd841d0-39f4-4ac6-bf49-de9879a7396c · question 69b0d79d · IBN 11305-DC
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