Section 3: Measurement of Lengths and Angles in Circles
To-Do Date: Thu Feb 24 2022 04:59:00 GMT+0000 (Coordinated Universal Time)Standards:
3.3.1 Determine whether a particular point lies on a given circle.
3.3.2 Translate between the geometric and algebraic representations of a circle.
3.3.3 Prove that any two circles are similar.
3.3.4 Determine the measure of a central angle or the circular arc it intercepts.
3.3.5 Determine the measure of an inscribed angle or the circular arc it intercepts.
3.3.6 Determine the length of a circular arc.
3.3.7 Construct a line, ray, or line segment tangent to a circle.
3.3.8 Solve a system of equations consisting of a linear equation and the equation of a circle.
Essential Question:
- How can I use the Pythagorean Theorem to derive the equation of a circle?
- How are the graph of a circle and its equation related?
- How are the equation of a circle and its graph related?
- How can I write the equation of a circle given information about the center and radius?
- How do you convert the standard form of a circle to general form?
- How do you convert the general form of a circle to standard form?
- How do you use a coordinate proof to determine whether or not a given point lies on a given circle in a coordinate plane?
- How can I determine the intersection of a line and a quadratic figure?
- How can we apply the properties of chords, tangents, and secants to determine the length of various segments?
- How do you find the lengths of chords in a circle?
- How do chords related to the intercepted arcs?
- How do we find the length of an arc of a circle?
- How do you find the area of a sector of a circle?
- How do you find the area of a segment of a circle?