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Circle Concept Map

Justine Baker

Period 5

Circles

Radius

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

Tangent

A line that passes through a circle at one point.

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

Center

Secant

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

A line that passes through a circle at two points.

Sector

Diameter

The area between two radii and the arc.

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

h

Basic Parts of a Circle

Chord

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

Proof

  • 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

Inscribed Angles

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

All Circles are Similar

Made with two chords or two secants in a circle

Types of Angles in a Circle

Central Angles

Created by the angle of two radiuses in a circle

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

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

Unit Circle

When a circle has the radius of 1.

Circumscribed Constructions

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

Radians

Circumcenter

A pure measure based on the radius of a circle.

1 Radian is equal to about 57.2958 degrees.

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

Other

Constructions of a Circle

Inscribed Construction

Orthocenter

The intersection of three altitudes.

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

Centroids

The intersection of all straight lines that divide X.

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

Pi

Incenter

The center of the circle inside the polygon.

Formulas

Tangent Construction

When a tangent is created on a circle.

Circles are round

Formula for Circumference

Relationship with the Radius

Relationship with the Diameter

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

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

Area Formula

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