If point P is at the center of the circle, and = 12 inches and arc AB = 60°, what is the length of line segment ?

Question

If point P is at the center of the circle, and  = 12 inches and arc AB = 60°, what is the length of line segment  ?

anonymous · Answer

attachment

anonymous · Answer

Possible answers

A. 4.5 inches
B. 6 inches
C. 9 inches
D. 12 inches

mathstudent55 · Answer

Is r = 12 in.?

mathstudent55 · Answer

If m(arc)AB = 60 deg, then m<APB = 60. Since PA and PB are radii of the same circle, they are congruent. That makes angles PAB and BAP congruent. The sum of their measures is 120 so each measures 60 degrees. That means the small triangle has all angles of 60 degrees and is equilateral, so all sides measure 12 in.