Circle Terminology:
Center: The point at the center of the circle.
Radius: The distance from the center to any point on the circle.
Diameter: The distance across the circle passing through the center (2 times the radius).
Chord: A line segment connecting two points on the circle.
Arc: A part of the circumference of the circle.
Sector: The region enclosed by two radii and the corresponding arc.
Circle Formulas:
Circumference (C): C = 2πr or C = πd (where r is the radius and d is the diameter).
Area (A): A = πr^2.
Central Angles and Arcs:
Central Angle: An angle whose vertex is at the center of the circle.
Arc Measure: The measure of the central angle that intercepts the arc.
Arc Length: The distance along the circumference of the circle.
Arc Length = (Arc Measure / 360) * Circumference.
Inscribed Angles and Arcs:
Inscribed Angle: An angle formed by two chords with its vertex on the circle.
Inscribed Angle Theorem: An inscribed angle is half the measure of its intercepted arc.
Intercepted Arc: The arc that lies between the endpoints of the inscribed angle.
Tangents:
Tangent: A line that intersects the circle at exactly one point (the point of tangency).
Tangent Theorem: A tangent line is perpendicular to the radius drawn to the point of tangency.
Secants:
Secant: A line that intersects the circle at two points.
Intersecting Chord Theorem: The product of the lengths of the two segments of a secant is equal to the product of the lengths of its external segment.
Relationships Between Angles and Arcs:
Angle-Arc Relationship: The measure of an inscribed angle is half the measure of its intercepted arc.
Angle in a Semicircle: An angle inscribed in a semicircle is a right angle (90 degrees).
Circle Construction:
Circumscribed Circle: A circle that passes through all the vertices of a polygon.
Incircle: A circle that is tangent to all the sides of a polygon.
Remember to practice solving problems involving these concepts, including finding angles, arc measures, lengths, and areas of circles. Additionally, review the properties and relationships between angles and arcs in different scenarios. Good luck with your study and the test!