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.
![### Determine the Equation of the Circle Graphed Below
In the image provided, there is a graph displaying a circle on a coordinate plane. Here are the details and steps to determine the equation of the circle:
1. **Coordinate Plane:**
- The coordinate plane features an x-axis that ranges from -10 to 10 and a y-axis that also ranges from -10 to 10.
- There is a grid background that aids in identifying points accurately.
2. **Circle:**
- The circle is centered at the point (-2, 6).
- The radius of the circle appears to be 2 units since the circle intersects the y-axis at y = 8 and y = 4.
### Understanding the Circle Equation
The standard equation of a circle with center \((h, k)\) and radius \(r\) is:
\[
(x - h)^2 + (y - k)^2 = r^2
\]
### Applying this to the Given Graph
- **Center (h, k):** The center of the circle is at \((-2, 6)\).
- **Radius (r):** The radius of the circle is 2 units.
Using the standard form of the circle’s equation:
\[
(x - (-2))^2 + (y - 6)^2 = 2^2
\]
This simplifies to:
\[
(x + 2)^2 + (y - 6)^2 = 4
\]
### Final Equation
The equation of the circle based on the given graph is:
\[
(x + 2)^2 + (y - 6)^2 = 4
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