Questions and Answers
What is the area of a circle?
πr^2
What is the formula for the area of a sector?
central angle/360 * πr^2
What is the area of a segment?
central angle/360 * πr^2 - area of triangle
What is the circumference of a circle?
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What is the formula for arc length?
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What is the relationship between the central angle and the intercepted arc?
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What is the relationship of an inscribed angle to the intercepted arc?
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How is an angle formed by two chords calculated?
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How is an angle outside the circle formed by secants or tangents calculated?
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What is the formula for segment length inside a circle formed by two chords?
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What is the formula for segment length outside a circle formed by secants or tangents?
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A tangent line is always perpendicular to the radius.
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If radius bisects the chord, then it is perpendicular to the chord.
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Study Notes
Circle Area and Perimeter Formulas
- Area of a Circle: Calculated using the formula πr², where r is the radius.
- Circumference of a Circle: The distance around the circle is given by the formula 2πr.
Sector and Segment Formulas
- Area of a Sector: Determined by the formula (central angle/360) * πr².
- Area of a Segment: This represents the area of the sector minus the area of the triangle formed within it, calculated by (central angle/360) * πr² - area of triangle.
Angles Related to Arcs
- Central Angle: The angle formed at the circle's center, equal to the measure of the intercepted arc.
- Inscribed Angle: Formed by two chords and has its vertex on the circle; it measures half of the intercepted arc.
- Angle inside a Circle: Formed by the intersection of two chords, calculated as 1/2 (arc 1 + arc 2).
- Angle outside a Circle: Formed by tangents or secants, calculated as 1/2 (bigger arc - smaller arc).
Segment Lengths and Relationships
- Segment Length Inside Circle: When formed by two intersecting chords, the segments satisfy the relationship (part * part = part * part).
- Segment Length Outside Circle: In secant or tangent relationships outside the circle, the relationship is given by (part outside * whole = part outside * whole).
Tangent and Chord Properties
- Tangent and Radius: A tangent line to a circle is always perpendicular to the radius at the point of contact.
- Chord and Radius Relationship: When a radius bisects a chord, it is perpendicular to that chord.
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Description
Test your understanding of circle area formulas, perimeter calculations, and the relationships between angles and arcs. This quiz covers essential concepts such as sectors, segments, and various types of angles related to circles.
