6 Questions
What is the term for the distance from the center of a circle to any point on the circle?
Radius
What is the formula for the area of a circle?
πr^2
What is the term for the angle formed by a tangent and a chord at the point of intersection?
Alternate Segment
What is the term for the line that joins the centers of two intersecting circles and passes through the points of intersection?
Chord
In which field of study are circles used in the design and construction of circular structures, such as bridges, tunnels, and pipes?
Engineering
What is the name of the theorem that states that the angle at the center of a circle is twice the angle at the circumference?
Inscribed Angle Theorem
Study Notes
Properties of Circles
- A circle is a set of points equidistant from a fixed point called the center.
- The distance from the center to any point on the circle is called the radius.
- The distance around the circle is called the circumference.
Circle Formulas
- Circumference (C) = 2 × π × radius (r) = 2 × πr
- Area (A) = π × radius^2 (r^2) = πr^2
- Diameter (d) = 2 × radius (r) = 2r
Circle Theorems
- Inscribed Angle Theorem: The angle at the center of a circle is twice the angle at the circumference.
- Alternate Segment Theorem: The angle between a tangent and a chord is equal to the angle in the alternate segment.
- Circle-Circle Intersection Theorem: If two circles intersect, the line joining their centers passes through the intersection points.
Circle Applications
- Geometry: Circles are used in geometric constructions, trigonometry, and analytic geometry.
- Engineering: Circles are used in design and construction of circular structures, such as bridges, tunnels, and pipes.
- Real-World: Circles are found in nature (e.g., sun, moon, eyes) and in human-made objects (e.g., wheels, gears, coins).
Test your knowledge of circles, including their properties, formulas, theorems, and real-world applications. Learn about the center, radius, circumference, and diameter of circles, as well as their uses in geometry, engineering, and everyday life.
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