- 210 feet.Each goat will have a circle with a diameter that is twice
the length of its leash (which is the radius). Izzy needs 80 feet, Eli
needs 60 feet, and Pat needs 40 feet. Draw these three circles so
they each have 15 feet between them. The sum of their diameters
and the two 15-foot gaps between them is 210 feet.
Set 77
- x= 16.Don’t get confused by the triangle shape that surrounds the
circle. Instead, think of these legs as rays or lines that intercept the
circle at one point and meet at the same exterior point. Remember
from page 202 that tangent lines drawn from a single exterior
point are congruent to each of their points of interception with the
circle. Therefore, AFis congruent to AB, EFis congruent to ED,
CBis congruent to CD,ABis 4, and DEis the difference of CE
and CD, or 12; xis 4 plus 12, or 16. - Radius P = 0.25.The diameter of O is half the diameter of
M. Therefore, the diameter of O is 1 in. The diameter of P
is half the diameter of O. Therefore, the diameter of P is 0.5
inches, making the radius 0.25. - B. Watch out for the trap! Choices aand dshow you circles with
diameters. Choices band cshow you a radius. Use the Pythagorean
theorem to find the length of each circle’s radius:
A: 7^2 + b^2 = ( 74 )^2. 49 + b^2 = 74. b^2 = 25. b= 5. Radius= 5.
B: 1^2 + ( 24 )^2 = c^2. 1 + 24 = c^2. 25 = c^2. 5 = c. Radius= ^12 (5) = 2.5.
C: 10^2 + b^2 = (10 2 )^2. 100 + b^2 = 200. b^2 = 100. b= 10.
Radius= ^12 (10) = 5.
D: 2.5^2 + (18.75)^2 = c^2. 6.25 + 18.75 = c^2. 25 = c^2. 5 = c.
Radius= 5.
Only B is not congruent to A, C, and D. - O.Parallel and congruent line segments form congruent arcs in
L. Two diameters form equal central angles which form congruent
arcs in P. Parallel tangent lines form congruent semi-circles in
N. Secants extending from a fixed exterior point form non-
congruent arcs in O.
501 Geometry Questions