Answer:
1) Segment AZ is a radius of Circle Z.
2) Suppose AZ = 8 cm, then DE = 16 cm.
3) What do you call AD? AD is a chord.
4) What do you call AD? AD is a chord.
5) Which point is the point of tangency? Point A
6) What kind of angle is Angle [tex]\sf ZA\;\!F[/tex]? Right angle
Step-by-step explanation:
Construction of the Circle
a) When drawing a circle, it is usual to label the centerpoint with the circle's name. Therefore, to draw Circle Z, draw a circle using a compass and label the center Z.
b) Mark point A on the circumference of Circle Z.
c) Draw point B inside Circle Z.
d) Draw point C outside Circle Z.
e) Connect points A and Z with a straight line segment.
f) A diameter of a circle is a straight line segment that connects two points on the circle's circumference and passes through the center of the circle. Therefore, to draw diameter DE, draw a straight line passing through the center of Circle Z and label its endpoints on the circumference as D and E.
g) To draw AD, connect points A and D with a straight line segment.
h) A tangent line of a circle is a straight line that intersects the circle at exactly one point, known as the point of tangency. Tangent lines are always perpendicular to the radius drawn to the point of tangency.
To draw tangent line [tex]\sf A\;\!F[/tex], draw a line that passes through point A and is perpendicular (at a right angle) to line segment AZ. Place point F on the tangent line. Connect points A and F with a line segment.
[tex]\dotfill[/tex]
Question 1)
[tex]\large\textsf{Segment AZ is a \boxed{\bf radius} of Circle Z.}[/tex]
Point Z is the center of Circle Z, and Point A is a point on its circumference. As the radius of a circle is the distance from the center of the circle to any point on its circumference, line segment AZ is the radius of Circle Z.
Question 2)
[tex]\large\textsf{Suppose $\sf AZ = 8 \;cm$, then $\sf DE = \boxed{\bf16 \;cm}$\;.}[/tex]
Line segment DE is the diameter of Circle Z. A diameter of a circle is equal to two radii. Since AZ is a radius of Circle Z and given that AZ = 8 cm, then the diameter is twice this, which equals 16 cm.
Question 3)
[tex]\large\textsf{What do you call AD? AD is a $\boxed{\bf chord}$\;.}[/tex]
A chord of a circle is a straight line segment connecting two points on the circle's circumference. As points A and D are on the circumference of Circle Z, this means that AD is a chord.
Question 4)
[tex]\large\textsf{What do you call AD? AD is a $\boxed{\bf chord}$\;.}[/tex]
A chord of a circle is a straight line segment connecting two points on the circle's circumference. As points A and D are on the circumference of Circle Z, this means that AD is a chord.
Question 5)
[tex]\large\textsf{Which point is the point of tangency? $\boxed{\bf Point \;A}$}[/tex]
The point of tangency is the single point at which a straight line (tangent line) intersects a circle without crossing it. As tangent [tex]\sf A\;\!F[/tex] intersects Circle Z at point A, then point A is the point of tangency.
Question 6)
[tex]\large\textsf{What kind of angle is Angle ZA\:\!F? $\boxed{\bf Right\;angle}$}[/tex]
Tangent lines are always perpendicular (at right angles) to the radius drawn to the point of tangency. Since AZ is the radius of Circle Z, point A is the point of tangency, and [tex]\sf A\;\!F[/tex] is the tangent line, then angle [tex]\sf ZA\;\!F[/tex] is a right angle.
