#### Math - 2017-18

# G.11 and *G.11 - Circle Properties

**G.11** The student will **use **angles, arcs, chords,
tangents, and secants to

a) **investigate**, **verify**, and **apply** properties of
circles;

b) **solve **real-world problems involving
properties of circles; and

c) **find **arc lengths and areas of sectors in
circles.

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.

**Bloom's Level:** Evaluate

*Adopted: 2009*

### 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

- Many relationships exist between and among
angles, arcs, secants, chords, and tangents of a circle.
- All circles are similar.
- A chord is part of a secant.
- Real-world applications may be drawn from architecture,
art, and construction.

· 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

**Review Area and Circumference of a Circle**

G.11a_{1}
**Find** the lengths, angle measures,
and arc measures associated with central angles

G.11c_{1}
**Calculate** the area of a
sector and length of an arc of a circle, using proportions.

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

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

G.11b_{1}
**Solve** real-world problems
associated with circles, using properties of angles, lines, and arcs.

G.11a_{2}
**Find** the lengths, angle
measures, and arc measures associated with 2 intersecting chords

G.11a_{3} **Find**
the lengths, angle measures, and arc measures associated with 2
intersecting secants

G.11a_{4} **Find**
the lengths, angle measures, and arc measures associated with intersecting
secant and tangent

G.11a_{5} **Find**
the lengths, angle measures, and arc measures associated with 2
intersecting tangents

G.11a_{6} **Find**
the lengths, angle measures, and arc measures associated with inscribed
angles

· 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.11b_{2} **Solve**
real-world problems associated with circles, using properties of angles, lines,
and arcs.

G.11a_{7} **Verify**
properties of circles, using deductive reasoning algebraic, and coordinate
methods.

·
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: Feb 22, 2018*