Victory for the ACT Student Text 15e

M ATH Q UIZZES • 267

EXPLANATIONS

 –Š‡ ϐ‹‰—”‡ „‡Ž‘™ǡ PQ circle O at point S circle O at point T . If the radius of circle O is 2, what is the area of the shaded portion ‘ˆ –Š‡ ϐ‹‰—”‡ǫ ‹• –ƒ‰‡– –‘ and QR ‹• –ƒ‰‡– –‘

20.

20. (J) Mathematics/Geometry/Complex

Figures and Lines and Angles and Circles The radii OS and OT ˆ‘” ”‹‰Š– ƒ‰Ž‡• ™‹–Š PQ and QR ǡ ”‡•’‡…–‹˜‡Ž›Ǥ ‘•‡“—‡–Ž›ǡ ™‡ ‘™ –Š‡ ‡ƒ•—”‡• ‘ˆ –Š”‡‡ ‘ˆ –Š‡ ƒ‰Ž‡• ‹ –Š‡ “—ƒ†”‹Žƒ–‡”ƒŽ SQTO : 90°, 90°, and 60°. Since the sum of –Š‡ ‹–‡”‹‘” ƒ‰Ž‡• ‘ˆ ƒ “—ƒ†”‹Žƒ–‡”ƒŽ –‘–ƒŽ 360°, 90 90 60 c c c & SOT 360 c + . SOT 120 c + Since 360 120 3 1 c c , the shaded area is equal to one-third of the area of the circle: 3 1 (2) 3 4 2 r r = .

F. 3 π G. 3 2 π H. π J. 3 4 π K. 2 π