Circle Properties — SAT Math Explained
Key characteristics and relationships in circles, including radius, diameter, chords, tangents, arcs, sectors, and the special angle relationships created by these elements.
The Core Idea
A circle's fundamental property is that every point on it is exactly the same distance (radius) from the center. All other circle relationships flow from this simple definition.
Key Vocabulary
Distance from center to any point on the circle
Distance across the circle through the center — d = 2r
A line segment with both endpoints on the circle
A portion of the circle's circumference
A line that touches the circle at exactly one point — perpendicular to the radius at that point
A line that intersects the circle at two points
An angle with vertex at the center — its measure equals the arc it intercepts
An angle with vertex on the circle — its measure is HALF the intercepted arc
Key Relationships
An inscribed angle is half the central angle intercepting the same arc
Any inscribed angle in a semicircle is exactly 90°
A tangent line is always perpendicular to the radius drawn to the point of tangency
Two chords intersecting inside a circle: the products of their segments are equal
Common Errors to Avoid
Confusing radius and diameter in formulas
Thinking inscribed angles equal the arc (they're half the arc)
Using diameter instead of radius in area and circumference formulas
Practice: Circle Properties
5 SAT-style questions. Select your answer and get an instant explanation.
How many degrees in a full circle?
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