10.1 Circle Basics
Notes
A circle is all points in a plane at a fixed distance (the radius) from a center.
- A diameter passes through the center: $d = 2r$.
- A chord joins two points on the circle. A diameter is the longest chord.
- A secant is a line that crosses the circle twice. A tangent touches it at exactly one point, the point of tangency.
- Circumference: $C = 2\pi r = \pi d$.
- Example: a circle with diameter 14 has radius 7 and circumference $14\pi \approx 44.0$.
Practice
A circle has a radius of 9. What is its diameter?
$d = 2r = 18$.
What is a segment with both endpoints on a circle called?
A chord joins two points on a circle. A secant is a line, not a segment ending on the circle.
A circle has a circumference of $30\pi$. What is its radius?
$2\pi r = 30\pi$, so $r = 15$.
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