Questions and Answers
What is the formula when the vertex is in the center of the circle?
What is the formula when the vertex is on the circle?
What is the formula when the vertex is inside the circle?
What is the formula when the vertex is outside the circle?
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What is a secant?
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What is a tangent?
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What is a chord?
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What is the definition of a circle?
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What is the center of a circle?
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What is the diameter?
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What is the radius?
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What is a central angle?
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What is a semicircle?
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What is a minor arc?
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What is a major arc?
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What is the intersecting chords formula?
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What is the 2 secants formula?
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What is the Tangent and secant formula?
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What is the formula for abc?
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Study Notes
Circle Geometry Basics
- Vertex in the Center: When the vertex is at the center, the measure of the angle is equal to the measure of the intercepted arc.
- Vertex on the Circle: For a vertex located on the circle, the angle's measure is half of the measure of the intercepted arc.
- Vertex Inside the Circle: If the vertex is inside the circle, the angle measure equals half the sum of the measures of the intercepted arcs.
- Vertex Outside the Circle: When the vertex is outside the circle, the angle's measure is half the difference between the measures of the intercepted arcs.
Circle Line Definitions
- Secant: A line that crosses a circle at two distinct points, creating a segment.
- Tangent: A line, ray, or segment that touches the circle at exactly one point, known as the point of tangency.
- Chord: A segment with both endpoints located on the circle.
Circle Components
- Circle: Defined as a collection of points equidistant from a central point.
- Center: The central point from which all points on the circle are equidistant.
- Diameter: The line segment that passes through the center of the circle, connecting two points on the circle.
- Radius: Half the length of the diameter, extending from the center to any point on the circle.
Angle Measurements
- Central Angle: An angle formed by two radii with its vertex at the center of the circle.
- Semicircle: Represents half of a circle's total area.
- Minor Arc: An arc measuring less than 180 degrees of the circle.
- Major Arc: An arc that measures more than 180 degrees.
Formulas Related to Circles
- Intersecting Chords Formula: The product of the segments of one chord equals the product of the segments of the other chord.
- Two Secants Formula: The product of the external segment and the whole length of one secant equals the product of the external segment and the whole length of another secant.
- Tangent and Secant Formula: The square of the tangent length equals the product of the length of the external segment and the total length of the secant.
- Quadratic Formula: Used to find the roots of a quadratic equation, expressed as x = (-b ± √(b² - 4ac)) / (2a).
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Description
Prepare for your Geometry Chapter 12 test with these flashcards. They cover important concepts such as the properties of angles formed by intersecting lines and circles. Review definitions and formulas essential for understanding circular geometry.
