Question

geometry
name
date
period
practice: parts of a circle

1. use the image to name the coordinates (x, y) of each of the following points, the first one has been provided for you.

center
(3, 3)
endpoints of a diameter
a point of tangency
endpoints of a chord that is not a diameter
endpoints of a radius
a point inside the circle
a point outside the circle

1. using the image to the right, identify the following parts of the circle.

chord
center
secant line
point of tangency
tangent line
major arc
diameter
minor arc
radius
semicircle

1. given each part of the circle, provide the correct term that best describes the part.

\\(overline{cd}\\)
\\(overleftrightarrow{fg}\\)
\\(overline{ec}\\)
\\(overline{ab}\\)
\\(overarc{eb}\\)
\\(overarc{ecb}\\)
h
a

Explanation:

Step1: Analyze first circle (grid)

Identify points from the coordinate grid:

• Endpoints of diameter: e.g., $(0,3)$ and $(6,3)$ (horizontal diameter through center)
• Point of tangency: $(3,0)$ (where circle touches x-axis)
• Non-diameter chord endpoints: e.g., $(0,3)$ and $(3,0)$
• Radius endpoints: e.g., $(3,3)$ and $(6,3)$ (center to circle edge)
• Inside point: e.g., $(3,2)$ (within circle bounds)
• Outside point: e.g., $(0,0)$ (outside circle bounds)

Step2: Analyze second circle (labeled)

Match parts to definitions:

• Chord: $\overline{ED}$ (line segment with both ends on circle)
• Secant line: $\overleftrightarrow{KJ}$ (line passing through two circle points)
• Tangent line: $\overleftrightarrow{AC}$ (line touching circle at 1 point)
• Diameter: $\overline{FH}$ (chord passing through center $G$)
• Radius: $\overline{GB}$ (segment from center to circle edge)
• Point of tangency: $B$ (where tangent meets circle)
• Major arc: $\overset{\frown}{EDB}$ (arc longer than semicircle)
• Minor arc: $\overset{\frown}{ED}$ (arc shorter than semicircle)
• Semicircle: $\overset{\frown}{FDB}$ (half-circle arc through diameter endpoints)

Step3: Analyze third circle (labeled)

Match parts to definitions:

• $\overline{CD}$: Chord (segment with both ends on circle)
• $\overline{EC}$: Chord (segment with both ends on circle)
• $\overset{\frown}{EB}$: Minor arc (short arc between $E$ and $B$)
• $H$: Point of tangency (where tangent meets circle)
• $\overleftrightarrow{FG}$: Tangent line (line touching circle at 1 point)
• $\overline{AB}$: Radius (segment from center $A$ to circle edge)
• $\overset{\frown}{ECB}$: Major arc (long arc through $E, C, B$)
• $A$: Center (middle point of the circle)

Answer:

Question 1

• Endpoints of a diameter: $(0, 3)$ and $(6, 3)$
• A point of tangency: $(3, 0)$
• Endpoints of a chord that is not a diameter: $(0, 3)$ and $(3, 0)$
• Endpoints of a radius: $(3, 3)$ and $(6, 3)$
• A point inside the circle: $(3, 2)$
• A point outside the circle: $(0, 0)$

Question 2

• Chord: $\overline{ED}$
• Secant line: $\overleftrightarrow{KJ}$
• Tangent line: $\overleftrightarrow{AC}$
• Diameter: $\overline{FH}$
• Radius: $\overline{GB}$
• Point of Tangency: $B$
• Major arc: $\overset{\frown}{EDB}$
• Minor arc: $\overset{\frown}{ED}$
• Semicircle: $\overset{\frown}{FDB}$

Question 3

• $\overline{CD}$: Chord
• $\overline{EC}$: Chord
• $\overset{\frown}{EB}$: Minor Arc
• $H$: Point of Tangency
• $\overleftrightarrow{FG}$: Tangent Line
• $\overline{AB}$: Radius
• $\overset{\frown}{ECB}$: Major Arc
• $A$: Center