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Parts of a circle and basic properties
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Circle: The set of all points equidistant from a center point.
Radius: Distance from center to any point on the circle (symbol: )
Diameter: Distance across circle through center (symbol: )
Chord: Line segment connecting two points on the circle
A line that intersects the circle at two points
A circle has a radius of 5. Find the circumference and area.
Circumference:
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Tangent: A line that touches the circle at exactly one point
Tangent Property: A tangent line is perpendicular to the radius at the point of tangency.
Chord Property: A perpendicular from the center to a chord bisects the chord.
Equal Chords: Chords equidistant from the center are congruent.
The distance around a circle:
For a central angle of degrees:
Area:
Answer: Circumference = (or ≈ 31.4), Area = (or ≈ 78.5)
A circle has diameter 16. Find the length of an arc with central angle .
Step 1: Find the radius
Step 2: Use arc length formula
Answer: Arc length is (or ≈ 6.28)
A chord is 8 cm from the center of a circle with radius 10 cm. Find the length of the chord.
Draw a radius to the chord's endpoint and a perpendicular from center to chord.
This creates a right triangle:
Use Pythagorean Theorem:
Answer: The chord length is 12 cm