Circle Properties: Radius, Diameter, Arcs

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Questions and Answers

What is a circle?

The set of all points in a plane, equidistant from a given point.

What is the center of a circle?

The given point from which all points on the circle are equidistant; the circle is named by this point.

Define the radius of a circle.

The distance from the center to any point on the circle.

A _____ is a segment whose endpoints are on the circle.

<p>chord</p>
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Which term describes a chord that contains the center of the circle?

<p>Diameter (A)</p>
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What is a tangent in relation to a circle?

<p>A line, segment, or ray that intersects the circle at a single point.</p>
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A secant is a line that intersects a circle at exactly one point.

<p>False (B)</p>
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What is the circumference of a circle, and how is it calculated?

<p>The distance around a circle, calculated using the formula $C = \pi d$ or $C = 2 \pi r$.</p>
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Define pi ($\pi$).

<p>The ratio of a circle's circumference to its diameter.</p>
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An _____ is the part of the circle created by the central angle.

<p>arc</p>
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What is a minor arc?

<p>An arc that measures less than 180 degrees.</p>
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What distinguishes a major arc?

<p>An arc that measures between 180 and 360 degrees.</p>
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What is the term for half of a circle, which measures exactly 180 degrees?

<p>Semicircle (C)</p>
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What is arc length?

<p>The length of an arc between two points on a circle.</p>
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What does arc measure represent?

<p>The number of degrees that an arc occupies on a circle.</p>
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A _____ angle is an angle whose vertex is the center of the circle.

<p>central</p>
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An inscribed angle is an angle whose vertex is the center of the circle.

<p>False (B)</p>
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What defines a circle?

<p>The set of all points in a plane that are equidistant from a given point (the center).</p>
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What is the center of a circle?

<p>The fixed point from which all points on the circle are equidistant. A circle is typically named by its center point.</p>
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Define the radius of a circle.

<p>The distance from the center of the circle to any point on the circle.</p>
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What is a chord of a circle?

<p>A line segment whose endpoints both lie on the circle.</p>
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Define the diameter of a circle.

<p>A chord that passes through the center of the circle.</p>
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What is a tangent to a circle?

<p>A line, segment, or ray in the plane of the circle that intersects the circle at exactly one point.</p>
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What is a secant line in relation to a circle?

<p>A line that intersects a circle at exactly two points.</p>
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What is the circumference of a circle?

<p>The distance around the circle (C)</p>
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What mathematical constant is defined as the ratio of a circle's circumference to its diameter?

<p>Pi ($\pi$)</p>
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What is an arc of a circle?

<p>A portion of the circumference of a circle between two points on the circle.</p>
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Which term describes an arc whose measure is less than 180 degrees?

<p>Minor arc (B)</p>
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What defines a major arc?

<p>An arc whose measure is greater than 180 degrees but less than 360 degrees.</p>
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What is a semicircle?

<p>An arc of a circle that measures exactly 180 degrees; it is half of a circle.</p>
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What is arc length?

<p>The physical distance along the curved path of an arc.</p>
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What is arc measure?

<p>The measure of the central angle that intercepts the arc, measured in degrees.</p>
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What is a central angle in a circle?

<p>An angle whose vertex is the center of the circle and whose sides are radii intersecting the circle at two points.</p>
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What is an inscribed angle?

<p>An angle whose vertex lies on the circle and whose sides are chords of the circle.</p>
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What is a circle?

<p>The set of all points in a plane, equidistant from a given point.</p>
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The _____ is the given point by which a circle is named.

<p>center</p>
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What term describes the distance from the center to any point on the circle?

<p>Radius (C)</p>
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A chord is a segment whose endpoints are on the circle.

<p>True (A)</p>
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What defines a diameter in a circle?

<p>A chord that contains the center of the circle.</p>
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A line, segment, or ray that intersects the circle at a single point is called a _____.

<p>tangent</p>
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Which term describes a line that intersects a circle at exactly two points?

<p>Secant (D)</p>
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What is the circumference of a circle, and what are the formulas to calculate it?

<p>The distance around a circle. Formulas: $C = \pi d$ or $C = 2\pi r$.</p>
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Pi ($\pi$) is the ratio of a circle's diameter to its circumference.

<p>False (B)</p>
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The part of the circle created by a central angle is known as an _____.

<p>arc</p>
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What is a minor arc?

<p>An arc that measures less than 180 degrees.</p>
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An arc that measures between 180 and 360 degrees is called a:

<p>Major arc (A)</p>
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What is a semicircle?

<p>Half of a circle / measures exactly 180 degrees.</p>
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The _____ _____ is the length of an arc between two points on a circle.

<p>arc length</p>
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Arc measure refers to the length of an arc in units like centimeters or inches.

<p>False (B)</p>
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What distinguishes a central angle?

<p>An angle whose vertex is the center of the circle.</p>
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An angle whose vertex is on the circle is called a(n):

<p>Inscribed angle (C)</p>
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Flashcards

Circle

The set of all points in a plane equidistant from a given point.

Center

The given point, what the circle is named by.

Radius

The distance from the center to any point on the circle.

Chord

A segment whose endpoints are on the circle.

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Diameter

A chord that contains the center of the circle.

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Tangent

A line, segment, or ray that intersects the circle at a single point.

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Secant

A line that intersects a circle at exactly 2 points.

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Circumference

The area around a circle (Ï€d or 2Ï€r).

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Pi (Ï€)

The ratio of a circle's circumference to its diameter.

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Arc

The part of the circle created by the central angle.

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Minor Arc

An arc that measures less than 180 degrees.

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Major Arc

An arc that measures between 180 and 360 degrees.

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Semicircle

Half of the circle; measures exactly 180 degrees.

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Arc Length

The length of an arc between two points on a circle.

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Arc Measure

The number of degrees that an arc occupies on a circle.

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Central Angle

An angle whose vertex is the center of the circle.

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Inscribed Angle

An angle whose vertex is on the circle.

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Study Notes

  • A circle is all points in a plane at the same distance from a specific point.
  • The center is the point used to name a circle.
  • The radius is the distance between the center and any point on the circle.
  • A chord is a line segment with both endpoints on the circle.
  • The diameter is a chord that passes through the circle's center.
  • A tangent is a line, segment, or ray that touches the circle at only one point.
  • A secant is a line that intersects the circle at two points.
  • Circumference is the distance around a circle, calculated as pi x d or 2 pi r.
  • Pi is the ratio of a circle's circumference to its diameter.
  • An arc is a portion of the circle formed by the central angle.

Minor Arc

  • A minor arc measures less than 180 degrees.

Major Arc

  • A major arc measures between 180 and 360 degrees.

Semicircle

  • A semicircle is half of a circle, measuring exactly 180 degrees.
  • Arc length is the distance along the arc between two points on the circle.
  • Arc measure is the number of degrees an arc covers on a circle.
  • A central angle is one where the vertex is at the circle's center.
  • An inscribed angle is one where the vertex lies on the circle itself.

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