**Circle Concept Map**

**Circles**

Basic Parts of a Circle

Types of Angles in a Circle

**Pi**

**Formulas**

Other

All Circles are Similar

h

Central Angles

Circles are round

Centroids

Proof

**Justine Baker**

Period 5

Period 5

Radius

Diameter

Chord

Tangent

Secant

Inscribed Angles

Created by the angle of two radiuses in a circle

Center

Made with two chords or two secants in a circle

Equal to half of the central angle it shares an arc with

Equal to twice the amount of the inscribed angle it shares an arc with

Formula for Circumference

Sector

Area Formula

The area between two radii and the arc.

A line that passes through a circle at two points.

A line that passes through a circle at one point.

A line segment that begin from the centre and touches any point on the circle.

Point in exact middle where all other points are equidistant away from.

Must pass through the centre of the circle. The Diameter is equal to twice the radius.

The chord joins any two points on a circle.

Arcs

Sections of the circumference

Equal to half of the inscribed angle it is related to or the same as the central angle it is related to

Constructions of a Circle

Circumscribed Constructions

When an object's points all rest on the circle that surrounds it.

Inscribed Construction

To draw a circle within a polygon where the enclosed circle touches the outer figure.

Tangent Construction

When a tangent is created on a circle.

Given a circle of radius r and a second circle of radius R

Dilate with a scale factor of k= R/r

The circles will map onto eachother by a dilation

All circles are similar

When bisected, it has a 90 degree angle with the center.

Relationship with the Diameter

Pi is used to calculate the circumference of a circle along with the diameter.

Relationship with the Radius

Pi is used to calculate the area and circumference with the radius.

Circumcenter

The center of the circle that is circumscribed around the polygon.

Incenter

The center of the circle inside the polygon.

The intersection of all straight lines that divide X.

Theorem=2[4r/3(pi)]

Orthocenter

The intersection of three altitudes.

Radians

A pure measure based on the radius of a circle.

1 Radian is equal to about 57.2958 degrees.

Unit Circle

When a circle has the radius of 1.

The 9-Point Circle

A circle that can come from any triangle that has nine points coming from:

The midpoint of each side

The foot of each altitude

The midpoint of the line segment from each vertex of the triangle and the orthocenter