sides as the Pythagorean triplet 6:8:10 to determine HJ is 10. Then set up the proportion
to determine FK: , so FK is 9 inches.
30 . H If the area of circle A is 36π, and the area of any circle is πr^2 , then the radius of circle A must
be 6. The diameter of circle A is therefore 12, and the diameter of circle B is half that, or 6.
The circumference of any circle is 2πr or πd, so the circumference of circle B is 6π. Choice
(H) is correct.
36 . H Plug in some numbers for the sides of the rectangle. Let’s say AB = 2. Since AB is of BC,
BC = 6, and AC = DE = 8. There are no restrictions on AE, so let’s say AE = CD = 3. The
area of ACDE = (8)(3) = 24. To find the area of ΔBCD, subtract the areas of triangles ABE
and CBD. The area of ABE = (3)(2) = 3, and the area of CBD = (3)(6) = 9, so the area of
BDE = 24 − (3 + 9) =12. Therefore, BDE is the area of ACDE.
39 . E If the length of AC is 8 , then the sides of the square must be 8 (splitting a square in half
gives you two 45-45-90 triangles with ratios 1:1: ). The radius of the circle is half the
length of the side of the square, so the radius is 4. The area of the circle is πr^2 = π(4^2 ) = 16π.
Therefore, the answer is (E).
48 . G Both RX and SX are radii of the circle, making them congruent. The triangle ΔRSX, therefore,
is isosceles, and SRX and RSX are congruent, each measuring 70°. The third angle RSX
= 180° − 2(70°) = 40° and is equal to the measure of . Choices (J) and (K) make the
incorrect pair of angles congruent.
54 . F Plug in values for the sides of the triangles: Triangle 1 can have a side length of 8 and
triangle 2 can have a side length of 6, making s = 2. Equilateral triangles can be split into two
30-60-90 triangles, thus their altitudes are (side length)× Triangle 1’s altitude is 4 ,
and triangle 2’s altitude is 3 , making the answer 4 − 3 = . Choice (G) confuses
30-60-90 with 45-45-90, and (H), (J), and (K) do not have a .
55 . D MN and OP are the radii of their respective circles, so the radius NY of circle N is 10 inches,
and radius OP of circle O is 8 inches. Given XY is 3 inches long, NX is 10 − 3 = 7 inches and
OY is 8 − 3 = 5 inches. Adding the three segments NX, XY, and OY, the length of NO is 7 + 3
