Circles SAT question

Math · Geometry and Trigonometry · Hard · Answer it here, explanation included.

A circle has center $O$ , and points $A$ and $B$ lie on the circle. The measure of arc $A B$ is $45^{\circ}$ and the length of arc $A B$ is $3$ inches. What is the circumference, in inches, of the circle?

ExplanationShow

Choice D is correct. It’s given that the measure of arc $A B$ is $4 5^{\circ}$ and the length of arc $A B$ is $3 inches$ . The arc measure of the full circle is $36 0^{\circ}$ . If $x$ represents the circumference, in inches, of the circle, it follows that $\frac{4 5 ^{\circ}}{36 0 ^{\circ}} = \frac{3 inches}{x inches}$ . This equation is equivalent to $\frac{45}{360} = \frac{3}{x}$ , or $\frac{1}{8} = \frac{3}{x}$ . Multiplying both sides of this equation by $8 x$ yields $1 (x) = 3 (8)$ , or $x = 24$ . Therefore, the circumference of the circle is $24 inches$ .

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 $A B$ .

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Circles SAT question

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