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Difficulty: MediumCircles

Match each geometric term related to circles with its correct mathematical definition.

  • ChordA line segment with both endpoints on the circle
  • SecantA straight line that intersects the circle at exactly two distinct points
  • TangentA straight line that touches the circle at exactly one point
  • DiameterA line segment passing through the center with endpoints on the circle

Answer

Chord matches with a line segment having endpoints on the circle. Secant matches with a straight line intersecting at two points. Tangent matches with a straight line touching at exactly one point. Diameter matches with a line segment passing through the center.
Each geometric term possesses a precise mathematical definition based on whether it is a finite segment or an infinite line, and how many distinct points it shares with the circle. A chord is a finite segment with two points on the circle, a diameter is a specific chord that passes through the center, a secant is an infinite line intersecting the circle at two points, and a tangent is an infinite line intersecting at exactly one point.

Step-by-Step Solution

1
Differentiate between lines and line segments in the definitions.
Identify that Chord and Diameter are finite line segments, while Secant and Tangent are straight lines extending infinitely.
This fundamental distinction splits the matching options into two distinct groups, making the problem easier to solve.
2
Distinguish between the two line segments (Chord and Diameter).
A diameter must pass through the center point, making it a specific type of chord. Therefore, 'Diameter' matches the definition mentioning the center, and 'Chord' matches the broader segment definition.
Both have endpoints on the circle, but only the diameter requires passing through the center point.
3
Distinguish between the two straight lines (Secant and Tangent).
A secant cuts through the circle at two points, while a tangent only touches the outer boundary at one point.
Counting the exact number of intersection points (two for a secant, one for a tangent) determines the correct match.

Key Concept

Geometric properties and terminology of lines and segments associated with circles
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Topics

Circles

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