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In the figure above, the circle with center O has a circumference of 50, and AB = BC. What is the length of arc AB?
Correct answer is '18.8'. Can you explain this answer?
Verified Answer
In the figure above, the circle with center O has a circumference of 5...
Let's start by drawing the three radii OA, OB, and OC. Since these radii are all congruent, and because AB = BC, the triangles AOB and COB are congruent (by the SSS Theorem). This implies that OB bisects angle ABC, so the base angles of both isosceles triangles must have measure 45°/2 = 22.5°. Therefore, angle AOB, which is the central angle for arc AB, must have measure 180° - 22.5° - 22.5° = 135°. Now we can use the fact that the circumference of the circle is 50 to find the length or arc AB.
Let
and cross multiply: 360x = 6,750Divide by 360: x = 75/4 = 18.75 or 18.8
Most Upvoted Answer
In the figure above, the circle with center O has a circumference of 5...
Let's start by drawing the three radii OA, OB, and OC. Since these radii are all congruent, and because AB = BC, the triangles AOB and COB are congruent (by the SSS Theorem). This implies that OB bisects angle ABC, so the base angles of both isosceles triangles must have measure 45°/2 = 22.5°. Therefore, angle AOB, which is the central angle for arc AB, must have measure 180° - 22.5° - 22.5° = 135°. Now we can use the fact that the circumference of the circle is 50 to find the length or arc AB.
Let
and cross multiply: 360x = 6,750Divide by 360: x = 75/4 = 18.75 or 18.8
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In the figure above, the circle with center O has a circumference of 50, and AB = BC. What is the length of arc AB?Correct answer is '18.8'. Can you explain this answer?
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In the figure above, the circle with center O has a circumference of 50, and AB = BC. What is the length of arc AB?Correct answer is '18.8'. Can you explain this answer? for SAT 2025 is part of SAT preparation. The Question and answers have been prepared according to the SAT exam syllabus. Information about In the figure above, the circle with center O has a circumference of 50, and AB = BC. What is the length of arc AB?Correct answer is '18.8'. Can you explain this answer? covers all topics & solutions for SAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the figure above, the circle with center O has a circumference of 50, and AB = BC. What is the length of arc AB?Correct answer is '18.8'. Can you explain this answer?.
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