A circle has center O , and points A and B lie on the circle. The measure of arc A

Question

A circle has center O , and points A and B lie on the circle. The measure of arc A B is 45 &#x02218; and the length of arc A B is 3 inches. What is the circumference, in inches, of the circle?

Accepted Answer

Choice D is correct. It&rsquo;s given that the measure of arc A B is 45 &#176; and the length of arc A B is 3 &#160; inches . The arc measure of the full circle is 360 &#176; . If x represents the circumference, in inches, of the circle, it follows that 45 &#176; 360 &#176; = 3 &#160; inches x &#160; inches . This equation is equivalent to 45 360 = 3 x , or 1 8 = 3 x . Multiplying both sides of this equation by 8 x yields 1 ( x ) = 3 ( 8 ) , or x = 24 . Therefore, the circumference of the circle is 24 &#160; inches . Choice A is incorrect. This is the length of arc A B . Choice B is incorrect and may result from multiplying the length of arc A B by 2 . Choice C is incorrect and may result from squaring the length of arc A B .

Question a-circ