Exploring Circles
Overview
A circle is named by its center, and almost every part of the circle is defined by how it relates to that center. This lesson names the parts — radius, chord, diameter, tangent, and secant — and establishes two facts used throughout the circle unit: a tangent is perpendicular to the radius at the point of tangency, and two tangent segments drawn from the same exterior point are congruent.
Vocabulary
- Circle
- The set of all points in a plane that are equidistant from a given point, called the center. A circle is named by its center.
- Radius
- A segment with one endpoint at the center of the circle and the other endpoint on the circle. All radii of a circle are congruent.
- Chord
- A segment whose two endpoints lie on the circle.
- Diameter
- A chord that passes through the center of the circle. The diameter is the longest chord of the circle; it is formed by two radii, so d = 2r.
- Tangent
- A line that intersects the circle at exactly one point, called the point of tangency. A tangent is perpendicular to the radius drawn to the point of tangency.
- Secant
- A line that intersects the circle at exactly two points. A secant contains a chord of the circle.
- Common Tangent
- A line that is tangent to two or more circles.
Main Ideas
- Every radius of a circle has the same length, and the diameter is twice the radius: d = 2r.
- A tangent touches the circle at exactly one point and never enters the interior of the circle.
- The radius to the point of tangency is perpendicular to the tangent, so tangent problems often hide a right triangle — look for the radius, the tangent segment, and the segment from the center to the exterior point.
- If two segments from the same exterior point are tangent to a circle, then they are congruent.
- A secant intersects the circle at two points; a chord is the part of a secant that lies inside the circle.
Lesson Notes
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Lesson Video
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