A circle has center O, and points A and B lie on the circle. The measure of arc AB is 45° and the length of arc AB is 3 inches. What is the circumference, in inches, of the circle?

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Accepted Answer

Choice D is correct. It’s given that the measure of arc AB is 45° and the length of arc AB is 3 inches. The arc measure of the full circle is 360°. If x represents the circumference, in inches, of the circle, it follows that 45° ⁄ 360° = 3 inches ⁄ x inches . This equation is equivalent to 45 ⁄ 360 = 3 ⁄ x , or 1 ⁄ 8 = 3 ⁄ x . Multiplying both sides of this equation by 8x yields 1(x) = 3(8), or x = 24. Therefore, the circumference of the circle is 24 inches. Distractor Explanations: Choice A is incorrect. This is the length of arc AB. Choice B is incorrect and may result from multiplying the length of arc AB by 2. Choice C is incorrect and may result from squaring the length of arc AB.

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