Angles in Circles
Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.
Arcs in Circles
A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.
Find the length s of the circular arc.
![The image depicts a circle with a central angle and a highlighted arc.
- The radius of the circle is labeled as 9 units.
- The central angle, marked at the center, is labeled as \(\frac{5\pi}{6}\) radians.
- The arc length corresponding to the central angle is highlighted in red and labeled as \(s\).
This diagram can be used to calculate the arc length \(s\) using the formula for arc length in a circle: \(s = r\theta\), where \(r\) is the radius and \(\theta\) is the angle in radians. In this case, the computation would be \(s = 9 \times \frac{5\pi}{6}\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5ed9e074-3bd4-4f31-9cb3-7306c76dde85%2Fd1647297-7d1b-49ce-8315-f34a13b4fa52%2Fv3x8e9m_processed.gif&w=3840&q=75)
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