Circles Notes and Worksheets - Lindsay Bowden - Free Printable

Let’s go step by step to fill in the blanks for each part of the circle. We’ll use simple definitions that match the pictures and standard geometry terms.

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1. Circle / Center of the Circle
Definition: “Set of all ________ that are the same ________ from the center point”
→ A circle is made of points (locations) that are all the same distance from the center.
✔ Fill in: points, distance

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2. Radius
Definition: “Line segment from the ________ to a point on the ________”
→ The radius goes from the center to any point on the edge (circumference).
✔ Fill in: center, circle

*(Note: Sometimes “circumference” is used, but since the worksheet says “on the ___”, and the picture shows point B on the circle, “circle” is correct here.)*

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3. Chord
Definition: “Line segment whose ________ are on the circle”
→ A chord connects two points on the circle. Those are called endpoints.
✔ Fill in: endpoints

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4. Diameter
Definition: “A ________ that passes through the ________ of the circle”
→ A diameter is a special chord — it goes through the center. So first blank = chord, second = center.
✔ Fill in: chord, center

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5. Secant Line
Definition: “A ________ that intersects the circle ________”
→ A secant is a line (not just a segment) that cuts through the circle at two points.
✔ Fill in: line, at two points

*(Sometimes written as “in two places” — but “at two points” is more precise and matches math language.)*

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6. Tangent Line / Point of Tangency
Definition: “A ________ that touches the circle ________ / Point where the tangent line touches”
→ A tangent is a line that touches the circle at exactly one point. That point is called the point of tangency.
✔ Fill in: line, at one point

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7. Arc
Definition: “Piece of the ________ (outside) of the circle *minor *major *semi-circle”
→ An arc is part of the circumference (the outer edge) of the circle.
✔ Fill in: circumference

*(“Outside” helps remind you it’s not the inside area — it’s the curved boundary.)*

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8. Sector
Definition: “Piece of the ________ of the circle”
→ A sector is like a pizza slice — it includes the center and two radii, so it’s a piece of the area or interior. But looking at the picture (shaded region O-N-P), it’s clearly an area bounded by two radii and an arc. In most middle/high school contexts, they say “piece of the area” or sometimes “region”. However, common phrasing in worksheets like this is:
✔ Fill in: area

*(Some might say “interior”, but “area” is simpler and matches student-level language.)*

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Now let’s compile all answers in order:

1. Circle/Center → points, distance
2. Radius → center, circle
3. Chord → endpoints
4. Diameter → chord, center
5. Secant Line → line, at two points
6. Tangent Line → line, at one point
7. Arc → circumference
8. Sector → area

Double-checking against standard definitions and the diagrams — everything matches.

Final Answer:
Circle/Center of the Circle: points, distance
Radius: center, circle
Chord: endpoints
Diameter: chord, center
Secant Line: line, at two points
Tangent Line/Point of Tangency: line, at one point
Arc: circumference
Sector: area