≡Mathematics EN 9th grade: Geometry of the Circle
1. Basic Elements
Circumference: set of points equidistant from a center.
Radius: segment from the center to the circumference.
Diameter: chord that passes through the center → \( d = 2r \)
Chord: segment that connects two points on the circumference.
Arc: part of the circumference between two points.
📌 Example:
If \( r = 5 \), then the diameter is \( d = 2 \times 5 = 10 \).
2. Corresponding Arcs and Chords
Equal chords correspond to equal arcs.
Larger chords correspond to larger arcs.
📌 Example:
If two chords have the same length, then the subtended arcs also have the same measure.
3. Lines and Circles
📍 Tangent Line
Touches the circle at a single point.
Is perpendicular to the radius at the point of tangency.
📌 Property:
If a line is tangent, then it forms a\( 90^\circ \) angle with the radius.
Example:
If a line touches the circle at A, then the radius to A is perpendicular to the line.
📍Secant Line
Intersects the circle at two points.
📍 Perpendicular Line to a Chord at its Midpoint
If a line passes through the midpoint of a chord and is perpendicular to it, then it passes through the center of the circle.
📌 Example:
If a chord AB has midpoint M, and a line is perpendicular at M, so this line contains the center.
Did you know?
