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Difficulty:
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Question Stats:
66% (02:13) correct
33% (02:05) wrong based on 3 sessions
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Points A, B, and C are three different points on a circle, which has area equal to \(64π\).
Quantity A
AB + AC
Quantity B
32
Quantity A
AB + AC
Quantity B
32
05 Oct 2025, 02:23
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Official Explanation
Use the area formula for a circle: Area \(= πr^2.\) So \(64π = πr^2,\) and \(r = 8.\) More importantly, the diameter \(= 2r = 2 × 8 = 16.\) There are many ways to place points A, B, and C, but the diagram may look like the above. If AB is a diameter, then AB = 16. But C is a point distinct from B, making AC not a diameter. Then AC < 16, because any chord in a circle that is not the diameter is smaller than the diameter. Therefore, AB + AC < 16 + 16 = 32, (B).
Answer: B
Use the area formula for a circle: Area \(= πr^2.\) So \(64π = πr^2,\) and \(r = 8.\) More importantly, the diameter \(= 2r = 2 × 8 = 16.\) There are many ways to place points A, B, and C, but the diagram may look like the above. If AB is a diameter, then AB = 16. But C is a point distinct from B, making AC not a diameter. Then AC < 16, because any chord in a circle that is not the diameter is smaller than the diameter. Therefore, AB + AC < 16 + 16 = 32, (B).
Answer: B
