#### Math - 2019-20

# G.11 - Circle Properties

G.11The student willsolveproblems, including practical problems, by applying properties of circles. This will includedetermininga) angle measures formed by intersecting chords, secants, and/or tangents;

b) lengths of segments formed by intersecting chords, secants, and/or tangents;

c)arc length;d) area of a sector.

*Adopted: 2016*

### BIG IDEAS

- I can place seats on a ferris wheel for perfect balance, get
the winning score in a dart game, and cut a pizza into equal pieces.

- I will
apply spatial reasoning and
visualization as ways to orient my thinking about the physical world,
especially in regards to circles since the world is not made up of straight
lines.

### UNDERSTANDING THE STANDARD

· All circles are similar.

· A chord is a line segment that joins any two points on a circle. A chord is a segment of a secant.

· Arcs can be measured in degrees or in units of length.

· Applications of the properties of circles may be drawn from architecture, art, and construction.

· Properties of circles can be verified using deductive reasoning, algebraic, and coordinate methods.

· Inscribed quadrilaterals have opposite angles that are supplementary.

· Properties associated with segment lengths can be verified using similar triangles.

· The ratio of the central angle to 360° is proportional to the ratio of the arc length to the circumference of the circle.

· The ratio of the central angle to 360° is proportional to the ratio of the area of the sector to the area of the circle.

· The construction for an inscribed equilateral triangle, square and regular hexagon can be justified using properties of a circle.### ESSENTIALS

**The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to**

·
G.11d_{1} **Calculate**
the area of a sector.

·
G.11c_{1} **Calculate**
the length of an arc of a circle.

· G.11b_{1} **Determine**
segment lengths associated with:

two intersecting chords;

two intersecting secants;

an intersecting secant and tangent; and

two intersecting tangents.

·
G.11a_{1} **Determine**
angle measures and arc measures associated with

two intersecting chords;

two intersecting secants;

an intersecting secant and tangent;

two intersecting tangents; and

central and inscribed angles.

·
G.11abcd_{1} **Solve**
problems, including practical problems, by **applying**
properties of circles.

### KEY VOCABULARY

point,
angle, arc, chord, segment, line, tangent, secant, circle, investigate, verify,
apply, solve, properties of circles, arc length, area, sector, length, angle
measure, arc measure, diameter, radius/radii, center, minor arc, major arc,
semicircle, intersecting chords,
intersecting secants, intersecting tangents, central angle, inscribed angle, inscribed,
circumscribed, intercepted arc, point of tangency, Pi, deductive reasoning,
algebraic methods, coordinate methods, similar

*Updated: Jul 30, 2019*