# SAT Math Multiple Choice Question 979: Answer and Explanation

### Test Information

Question: 979

15. If arc AB has a length of 12π and represents three-fourths of the circumference of circle O (not shown), what is the shortest distance between the endpoints of the arc?

• A. 4
• B. • C. 8
• D. Explanation:

D

Difficulty: Hard

Category: Additional Topics in Math / Geometry

Strategic Advice: Draw a sketch to visualize the situation and to reveal helpful hidden shapes.

Getting to the Answer: You're told that arc AB measures 12π and represents of a full circumference, which means it is the major arc and sits across from an internal angle that has a measure of . This, in turn, means minor arc AB is across from a 90° (right) angle, as shown here: Because of the full circumference is 12π, the full circumference itself must be 16π. A circle's circumference is equal to 2πr, so the radius of the circle is 8. and are both radii and therefore equal, so ΔABO is an isosceles right (and 45-45-90) triangle with sides in the ratio . The legs (radii) have length 8, so the length of the hypotenuse (which represents the shortest distance between the endpoints of the major arc) is . (D) is therefore correct.