Victory for the ACT Student Text 15e

V ICTORY P RACTICE T EST A NSWERS AND E XPLANATIONS • 457

23. (E) (p. 383) Mathematics/Geometry/Circles and Triangles/Pythagorean Theorem .

A diameter drawn perpendicular to the chord bisects the chord. Therefore, AB forms right triangle OEC with OC as the hypotenuse. Since OE 3 inches and CE theorem ( a b c 2 2 2 + = ): ( Hypotenuse) Leg Leg 2 2 2

bisects CD

. A constructed radius OC Ͷ inches, use the Pythagorean

^

h

^

h

=

+

1

2

^

h

^

h

^

h

OC OE CE x x x 3 4 25 5 2 2 2 2 2 2 ! = + = + = =

2

‹…‡ Ž‡‰–Š —•– „‡ ’‘•‹–‹˜‡ǡ –Š‡ ”ƒ†‹—• ‹• ͷǤ

The diagonals of a parallelogram bisect each other. Therefore:

24. (F) (p. 383) Mathematics/Geometry/Lines and Angles .

( 4 2 2 4 = + = + + = + ^ h DB DE 2 x x x x 4 2 2 8

)

= =

x x

2 6

3

25. (E) (p. 384) Mathematics/Geometry/Lines and Angles and Circles and Number and Quantity/Rates and Proportions . ‹…‡ ƒ ϐ‹‰—”‡ ‹•ǯ– ’”‘˜‹†‡†ǡ †”ƒ™ ‘‡ǣ

area of sector area of circle

x r 2 r

area of sector central angle

360 c

area of circle

r x x

c c

360 120

2

r

36 3 1 r

x

r

3 36

x

r

12