Learn about chords and arcs of a circle and their properties.
Example 1: Circle, Chord, and Arc
Define a circle, a chord, and an arc.
Circle: A circle is a set of all points in a plane that are at a fixed distance (radius) from a fixed point (center).
Chord: A chord is a line segment that connects two points on the circumference of a circle. The diameter is the longest chord, passing through the center.
Arc: An arc is a continuous part of the circumference of a circle. It is defined by two points on the circle.
Example 2: Perpendicular from Center to Chord
State the property of a perpendicular drawn from the center of a circle to a chord.
Property: The perpendicular drawn from the center of a circle to a chord **bisects** the chord.
Meaning: If you draw a line segment from the center (O) that hits the chord (AB) at a 90-degree angle at point M, then M is the midpoint of the chord AB. This means AM = MB.
Example 3: Converse of Perpendicular from Center to Chord
State the converse of the property of a perpendicular from the center to a chord.
Converse Property: The line segment joining the center of a circle to the midpoint of a chord is **perpendicular** to the chord.
Meaning: If you have a chord AB and M is its midpoint (AM = MB), then the line segment OM (connecting the center O to M) forms a 90-degree angle with the chord AB.
Example 4: Major and Minor Arcs
Explain the difference between a minor arc and a major arc.
Minor Arc: A minor arc is the shorter of the two arcs between two points on a circle. It is usually named using the two endpoints.
Major Arc: A major arc is the longer of the two arcs between two points on a circle. It is usually named using the two endpoints and one other point on the arc to indicate which longer path is meant.
Semicircle: If the two endpoints of an arc form a diameter, the two resulting arcs are semicircles, and they are congruent.
Practice Mode
Enter a simple problem about circle chords or arcs.
Note: This basic solver can provide definitions or properties based on keywords (e.g., "define chord", "perpendicular to chord property", "what is a major arc").
Related Concepts
Explore these related mathematical concepts to deepen your understanding of circles.
Radius
The distance from the center to any point on the circle.
Diameter
A chord passing through the center; twice the radius.
Circumference
The total distance around the circle.
Center
The fixed point from which all points on the circle are equidistant.
Sector
A region of a circle enclosed by two radii and an arc.
Segment
A region of a circle enclosed by a chord and an arc.
Tangent
A line that touches the circle at exactly one point.